/*
2018.12.2
今天自习课闲来无事，把部分学过的模板了打一遍，集中于此文件，便于未来复习
2018.12.3
继续补坑
2018.12.4
翘了一节微机课来补坑
2018.12.5
update lct
2018.12.6
update quickRead
2018.12.9
update sort
2018.12.12
update 时隔多天, update inv && suffixSort
2018.12.23
update string && Möbius
2019.01.21
准备期末考试，时隔一个月才来机房，然而期末依然炸了qwq
update 杜教筛
2019.02.14
update CG
2019.04.03
update splay FFT graph
2021.07.08
修改了部分单词拼写错误，觉得自己两年前就像个sb
*/
/*
所有代码未经编译，正确性未知，如有错误欢迎指正
code by Ηydra
*/
#include <algorithm>
#include <cctype>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <string>
#include <vector>
#define min(l, r) ((l) < (r) ? (l) : (r))
#define max(l, r) ((l) < (r) ? (r) : (l))
using std::swap;
namespace init
{
// Not Recommended
// #define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 21, stdin), p1 == p2) ? EOF : *p1++)
// char buf[1 << 21], *p1 = buf, *p2 = buf;
// 需C++11
template <typename T>
void rd(T &s)
{
bool p = 0;
char ch;
s = 0;
while (ch = getchar(), p |= ch == '-', !isdigit(ch))
;
while (s = s * 10 + ch - '0', isdigit(ch = getchar()))
;
s *= (p ? -1 : 1);
}
template <typename T, typename... Args>
void rd(T &s, Args &... args)
{
rd(s);
rd(args...);
}
// NOIP用
void rd(int &s)
{
s = 0;
int p = 0;
char ch;
while (ch = getchar(), p |= ch == '-', !isdigit(ch))
;
while (s = s * 10 + ch - '0', isdigit(ch = getchar()))
;
s *= (p ? -1 : 1);
}
char rdch_int()
{
char ch;
while (ch = getchar(), ch < '0' || ch > '9')
;
return ch;
}
char rdch_char()
{
char ch;
while (ch = getchar(), !isalpha(ch))
;
return ch;
}
} // namespace init
namespace segment_tree
{
#define mid(l, r) ((l + r) >> 1)
#define ls(x) ((x) << 1)
#define rs(x) (((x) << 1) | 1)
#define fa(x) ((x) >> 1)
#define len(x) (tree[x].r - tree[x].l + 1)
const int N = 1000000;
struct node
{
long long l, r, val;
long long lzy1, lzy2;
} tree[N << 4];
inline void updata(int x)
{
tree[x].val = (tree[ls(x)].val + tree[rs(x)].val);
}
inline void downdata(int x)
{
if (tree[x].lzy2 > 1)
{
tree[ls(x)].lzy2 *= tree[x].lzy2;
tree[rs(x)].lzy2 *= tree[x].lzy2;
tree[ls(x)].lzy1 *= tree[x].lzy2;
tree[rs(x)].lzy1 *= tree[x].lzy2;
tree[ls(x)].val *= tree[x].lzy2;
tree[rs(x)].val *= tree[x].lzy2;
}
tree[x].lzy2 = 1;
if (tree[x].lzy1)
{
tree[ls(x)].lzy1 += tree[x].lzy1;
tree[rs(x)].lzy1 += tree[x].lzy1;
tree[ls(x)].val += tree[x].lzy1 * len(ls(x));
tree[rs(x)].val += tree[x].lzy2 * len(rs(x));
}
tree[x].lzy1 = 0;
}
void build(int i, int l, int r)
{
tree[i].l = l;
tree[i].r = r;
tree[i].lzy1 = 0;
tree[i].lzy2 = 1;
if (l == r)
{
init::rd(tree[i].val);
return;
}
int m = mid(l, r);
build(ls(i), l, m),
build(rs(i), m + 1, r);
updata(i);
}
void add(int i, int l, int r, long long k)
{
if (tree[i].l == l && r == tree[i].r)
{
tree[i].val += k * len(i);
tree[i].lzy1 += k;
return;
}
downdata(i);
int m = mid(tree[i].l, tree[i].r);
if (l > m)
add(rs(i), l, r, k);
else if (r <= m)
add(ls(i), l, r, k);
else
add(ls(i), l, m, k),
add(rs(i), m + 1, r, k);
updata(i);
}
void mul(int i, int l, int r, long long k)
{
if (tree[i].l == l && r == tree[i].r)
{
tree[i].lzy1 *= k;
tree[i].val *= k;
tree[i].lzy2 *= k;
return;
}
downdata(i);
int m = mid(tree[i].l, tree[i].r);
if (l > m)
mul(rs(i), l, r, k);
else if (r <= m)
mul(ls(i), l, r, k);
else
mul(ls(i), l, m, k),
mul(rs(i), m + 1, r, k);
updata(i);
}
long long query(int i, int l, int r)
{
if (tree[i].l == l && tree[i].r == r)
return tree[i].val;
downdata(i);
int m = mid(tree[i].l, tree[i].r);
if (l > m)
return query(rs(i), l, r);
else if (r <= m)
return query(ls(i), l, r);
else
return query(ls(i), l, m) + query(rs(i), m + 1, r);
}
#undef ls
#undef rs
#undef mid
#undef fa
#undef len
} // namespace segment_tree
namespace fenwickTree
{
#define lowbit(x) ((x) & -(x))
const int N = 100000;
int tree[N];
int del1[N], del2[N];
int sum[N];
int tot;
void add(int *d, int x, int k)
{
while (x <= tot)
d[x] += k,
x += lowbit(x);
}
int query(int *d, int x)
{
int ans = 0;
while (x)
ans += d[x],
x -= lowbit(x);
return ans;
}
//单点修改 区间查询
void add_point_normal(int x, int k)
{
add(tree, x, k);
}
int query_interval_normal(int l, int r)
{
return query(tree, r) - query(tree, l - 1);
}
//区间修改 单点查询
void add_interval_normal(int l, int r, int k)
{
add(tree, l, k);
add(tree, r + 1, -k);
}
int query_point_normal(int x)
{
return query(tree, x);
}
//区间修改 区间查询
void add_interval_special(int l, int r, int k)
{
add(del1, l, k);
add(del1, r + 1, -k);
add(del2, l, k * l);
add(del2, r + 1, -k * (r + 1));
}
int query_interval_special(int l, int r)
{
return sum[r] + (r + 1) * query(del1, r) - query(del2, r) - (sum[l - 1] + l * query(del1, l - 1) - query(del2, l - 1));
}
//代替平衡树部分操作
int hs[N]; //大部分情况需将操作数离散化
void del(int x)
{
--sum[x];
add(tree, x, 1);
}
void insert(int x)
{
++sum[x];
add(tree, x, -1);
}
int find_rank(int x)
{
int ans = 0, cnt = 0;
for (int i = 21; i >= 0; --i)
{
ans += 1 << i;
if (ans > tot || cnt + tree[ans] >= x)
ans -= 1 << i;
else
cnt += tree[ans];
}
return hs[ans + 1];
}
int my_rank(int x)
{
int ans = 1;
--x;
while (x)
ans += tree[x],
x -= lowbit(x);
return ans;
}
int pre(int x)
{
insert(x);
int ans = find_rank(my_rank(x) - 1);
del(x);
return ans;
}
int nxt(int x)
{
insert(x);
int ans = find_rank(my_rank(x) + sum[x]);
del(x);
return ans;
}
#undef lowbit
} // namespace fenwickTree
namespace SPLAY
{
const int MAX = 200000;
int fa[MAX], val[MAX], sze[MAX], cnt[MAX], son[MAX][2];
int rt;
int tot = 0;
int fre[100000];
int top = 0;
int new_node()
{
return top ? fre[top--] : ++tot;
}
void updata(int x)
{
sze[x] = sze[son[x][0]] + sze[son[x][1]] + cnt[x];
}
void rotate(int x, int &k)
{
int y = fa[x], z = fa[y];
bool p = son[y][1] == x;
if (y == k)
k = x;
else
son[z][son[z][1] == y] = x;
fa[x] = z;
fa[y] = x;
fa[son[x][p ^ 1]] = y;
son[y][p] = son[x][p ^ 1];
son[x][p ^ 1] = y;
updata(y);
updata(x);
}
void splay(int x, int &k)
{
int y, z;
while (x != k)
{
y = fa[x], z = fa[y];
if (y != k)
{
if ((son[z][1] == y) == (son[y][1] == x))
rotate(y, k);
else
rotate(x, k);
}
rotate(x, k);
}
}
void insert(int &o, int x, int f)
{
if (!o)
{
o = new_node();
val[o] = x;
cnt[o] = 1;
sze[o] = 1;
son[o][0] = son[o][1] = 0;
fa[o] = f;
splay(o, rt);
}
else if (x == val[o])
{
++cnt[o];
splay(o, rt);
}
else
x < val[o] ? insert(son[o][0], x, o) : insert(son[o][1], x, o);
}
void find(int o, int x)
{
if (x == val[o])
splay(o, rt);
else
x < val[o] ? find(son[o][0], x) : find(son[o][1], x);
}
void merge(int l, int r)
{
if (!l || !r)
{
rt = l ^ r;
return;
}
int o = l;
while (son[o][1])
o = son[o][1];
splay(o, l);
rt = l;
son[l][1] = r;
fa[r] = l;
updata(rt);
}
void del(int x)
{
find(rt, x);
if (cnt[rt] > 1)
{
--cnt[rt];
--sze[rt];
return;
}
fre[++top] = rt;
fa[son[rt][0]] = fa[son[rt][1]] = 0;
merge(son[rt][0], son[rt][1]);
}
int my_rank(int x)
{
insert(rt, x, 0);
int ans = sze[son[rt][0]];
del(x);
return ans;
}
int find_rank(int o, int x)
{
return sze[son[o][0]] < x ? sze[son[o][0]] + cnt[o] >= x ? val[o] : find_rank(son[o][1], x - (sze[son[o][0]] + cnt[o])) : find_rank(son[o][0], x);
}
int pre(int x)
{
int o = rt, ans = -1;
while (o)
x > val[o] ? (ans = val[o], o = son[o][1]) : o = son[o][0];
return ans;
}
int nxt(int x)
{
int o = rt, ans = -1;
while (o)
x >= val[o] ? o = son[o][1] : (ans = val[o], o = son[o][0]);
return ans;
}
void dfs(int o)
{
if (!o)
return;
dfs(son[o][0]);
std::cout << val[o] << " ";
dfs(son[o][1]);
}
} // namespace SPLAY
namespace SPLAY_interval
{
const int MAXN = 5000000;
int fa[MAXN], son[MAXN][2], sze[MAXN], val[MAXN];
int tag1[MAXN], tag2[MAXN];
int sum[MAXN], maxl[MAXN], maxr[MAXN], maxsum[MAXN];
int fre[MAXN], cnt = 0, top = 0;
int rt;
int new_node()
{
return top ? fre[top--] : ++cnt;
}
#define mid(l, r) (((l) + (r)) >> 1)
#define ls(o) (son[o][0])
#define rs(o) (son[o][1])
void updata(int o)
{
sum[o] = sum[ls(o)] + sum[rs(o)] + val[o];
sze[o] = sze[ls(o)] + sze[rs(o)] + 1;
maxl[o] = max(maxl[ls(o)], sum[ls(o)] + val[o] + maxl[rs(o)]);
maxr[o] = max(maxr[rs(o)], sum[rs(o)] + val[o] + maxr[ls(o)]);
maxsum[o] = max(max(maxsum[ls(o)], maxsum[rs(o)]), maxr[ls(o)] + val[o] + maxl[rs(o)]);
}
void push_down(int o)
{
int v;
if (tag1[o])
{
int c = val[o];
if ((v = ls(o)))
{
tag1[v] = 1;
tag2[v] = 0;
val[v] = c;
sum[v] = c * sze[v];
maxl[v] = maxr[v] = (c > 0 ? sum[v] : 0);
maxsum[v] = (c > 0 ? sum[v] : c);
}
if ((v = rs(o)))
{
tag1[v] = 1;
tag2[v] = 0;
val[v] = c;
sum[v] = c * sze[v];
maxl[v] = maxr[v] = (c > 0 ? sum[v] : 0);
maxsum[v] = (c > 0 ? sum[v] : c);
}
tag1[o] = 0;
}
if (tag2[o])
{
if ((v = ls(o)))
{
tag2[v] ^= 1;
swap(ls(v), rs(v));
swap(maxl[v], maxr[v]);
}
if ((v = rs(o)))
{
tag2[v] ^= 1;
swap(ls(v), rs(v));
swap(maxl[v], maxr[v]);
}
tag2[o] = 0;
}
}
void rotate(int x, int &k)
{
int y = fa[x], z = fa[y];
int p = rs(y) == x;
if (y == k)
k = x;
else
son[z][rs(z) == y] = x;
fa[x] = z;
fa[y] = x;
fa[son[x][p ^ 1]] = y;
son[y][p] = son[x][p ^ 1];
son[x][p ^ 1] = y;
updata(y);
updata(x);
}
void splay(int x, int &k)
{
int y, z;
while (x != k)
{
y = fa[x], z = fa[y];
if (y != k)
rotate(ls(z) == y ^ ls(y) == x ? x : y, k);
rotate(x, k);
}
}
void init(int o)
{
fa[o] = son[o][0] = son[o][1] = tag1[o] = tag2[o] = sum[o] = maxl[o] = maxr[o] = maxsum[o] = 0;
}
void build(int &o, int l, int r, int *a, int f)
{
if (l > r)
return;
o = new_node();
int m = mid(l, r);
init(o);
fa[o] = f;
val[o] = a[m];
sze[o] = r - l + 1;
if (l == r)
{
sum[o] = maxsum[o] = val[o];
maxl[o] = maxr[o] = max(val[o], 0);
return;
}
build(ls(o), l, m - 1, a, o);
build(rs(o), m + 1, r, a, o);
updata(o);
}
int find(int k)
{
int o = rt;
while (true)
{
push_down(o);
if (sze[ls(o)] + 1 == k)
return o;
if (sze[ls(o)] + 1 > k)
o = ls(o);
else
k -= (sze[ls(o)] + 1), o = rs(o);
}
}
int split(int pos, int tot)
{
int l = find(pos), r = find(pos + tot + 1);
splay(l, rt);
splay(r, rs(l));
return ls(r);
}
void insert(int pos, int tot, int *a)
{
int l = find(pos + 1), r = find(pos + 2);
splay(l, rt);
splay(r, rs(l));
build(ls(r), 1, tot, a, r);
updata(r);
updata(l);
}
void dfs_del(int o)
{
if (!o)
return;
fre[++top] = o;
dfs_del(ls(o));
dfs_del(rs(o));
}
void del(int pos, int tot)
{
int o = split(pos, tot);
dfs_del(o);
ls(fa[o]) = 0;
updata(fa[o]);
updata(rt);
}
void modify(int pos, int tot, int c)
{
int o = split(pos, tot);
val[o] = c;
sum[o] = c * sze[o];
if (c > 0)
maxsum[o] = maxl[o] = maxr[o] = sum[o];
else
maxsum[o] = c, maxl[o] = maxr[o] = 0;
tag1[o] = 1;
tag2[o] = 0;
updata(fa[o]);
updata(rt);
}
void reverse(int pos, int tot)
{
int o = split(pos, tot);
tag2[o] ^= 1;
swap(maxl[o], maxr[o]);
swap(ls(o), rs(o));
updata(fa[o]);
updata(rt);
}
int get_sum(int pos, int tot)
{
int o = split(pos, tot);
return sum[o];
}
int max_sum()
{
return maxsum[rt];
}
void main(int *a, int n)
{
a[1] = a[n + 2] = maxsum[0] = -0x3f3fffff;
build(rt, 1, n + 2, a, 0);
}
#undef ls
#undef rs
#undef mid
} // namespace SPLAY_interval
namespace lct
{
const int N = 1000000;
int cnt;
int head[N], nxt[N], to[N];
int sze[N], son[N], dep[N], top[N], rk[N], id[N], fa[N], ed[N];
void dfs1(int u)
{
sze[u] = 1;
for (int i = head[u]; i; i = nxt[i])
{
int v = to[i];
if (v == fa[i])
continue;
dep[v] = dep[u] + 1;
fa[v] = u;
dfs1(v);
sze[u] += sze[v];
if (sze[v] > sze[son[u]])
son[u] = v;
}
}
void dfs2(int u, int t)
{
top[u] = t;
id[u] = ++cnt;
rk[cnt] = u;
if (son[u])
dfs2(son[u], t);
for (int i = head[u]; i; i = nxt[i])
{
int v = to[i];
if (v == fa[u] || v == son[u])
continue;
dfs2(v, v);
}
ed[u] = cnt;
}
void add1(int x, int y, int k)
{
while (top[x] != top[y])
{
if (dep[top[x]] < dep[top[y]])
std::swap(x, y);
fenwickTree::add_interval_special(id[top[x]], id[x], k);
x = fa[top[x]];
}
if (dep[x] < dep[y])
std::swap(x, y);
fenwickTree::add_interval_special(id[y], id[x], k);
}
int query1(int x, int y)
{
int ans = 0;
while (top[x] != top[y])
{
if (dep[top[x]] < dep[top[y]])
std::swap(x, y);
ans += fenwickTree::query_interval_special(id[top[x]], id[x]);
x = fa[top[x]];
}
if (dep[x] < dep[y])
std::swap(x, y);
ans += fenwickTree::query_interval_special(id[y], id[x]);
return ans;
}
void add2(int x, int k)
{
fenwickTree::add_interval_special(id[x], ed[x], k);
}
int query2(int x)
{
return fenwickTree::query_interval_special(id[x], ed[x]);
}
} // namespace lct
namespace eulerFunction
{
const int N = 10000000;
int vis[N];
int phi[N];
int pri[N], cnt;
long long SolveWithlogN(long long n)
{
int sum = n;
for (long long i = 1; i * i <= n; ++i)
if (n % i == 0)
{
sum -= sum / i;
while (n % i == 0)
n /= i;
}
if (n > 1)
sum -= sum / n;
return sum;
}
int main(int n)
{
vis[1] = 1;
for (int i = 2; i <= n; ++i)
{
if (!vis[i])
pri[++cnt] = i,
phi[i] = i - 1;
for (int j = i * 2; pri[j] * i <= n; ++j)
{
vis[pri[j] * i] = 1;
if (i % pri[j] == 0)
{
phi[i * pri[j]] = phi[i] * pri[j];
break;
}
else
phi[i * pri[j]] = phi[i] * phi[pri[j]];
}
}
return 0;
}
} // namespace eulerFunction
namespace prime
{
void solveWithN(int n)
{
eulerFunction::main(n);
}
bool solveWithsqrtN(long long n)
{
if (n == 1)
return 0;
for (long long i = 2; i * i <= n; ++i)
if (n % i == 0)
return 0;
return 1;
}
bool solve_develop(int n)
{
if (n == 1)
return 0;
if (n == 2 || n == 3)
return 1;
if (n % 6 != 1 && n % 6 != 5)
return 0;
for (long long i = 5; i * i <= n; i += 6)
if (n % i == 0 || n % (i + 2) == 0)
return 0;
return 1;
}
} // namespace prime
namespace qpow
{
//please use this when p approaches LONG_LONG_MAX
//warning : this function is very slow(logB)
long long mul(long long a, long long b, long long p)
{
long long s = 0;
for (; b; b >>= 1, a = (a + a) % p)
if (b & 1)
s = (s + a) % p;
return s;
}
long long pow_special(long long a, long long b, long long p)
{
long long s = 1;
for (; b; b >>= 1, a = mul(a, a, p))
if (b & 1)
s = mul(s, a, p);
return s;
}
long long pow_normal(long long a, long long b, long long p)
{
long long s = 1;
for (; b; b >>= 1, a = (a * a % p))
if (b & 1)
s = (s * a) % p;
return s;
}
} // namespace qpow
//haven't finished
namespace exgcd
{
typedef long long ll;
void exgcd(ll a, ll b, ll &x, ll &y, ll &gcd)
{
if (!b)
x = 1,
y = 0,
gcd = a;
else
exgcd(b, a % b, y, x, gcd),
y -= (a / b) * x;
}
// ax = 1 (mod p)
// (a, p) = 1
ll inv(ll a, ll p)
{
ll x, y, g;
exgcd(a, p, x, y, g);
if (g != 1)
return -1;
while (x < 0)
x += p;
return x;
}
} // namespace exgcd
namespace inv
{
typedef long long ll;
// p is a prime && (a, p) == 1
ll FermatLittleTheorem(ll a, ll p)
{
return qpow::pow_special(a, p - 2, p);
// return qpow::pow_normal(a, p - 2, p);
}
// (a, p) == 1
ll EulerTheorem(ll a, ll p)
{
return qpow::pow_special(a, eulerFunction::SolveWithlogN(p) - 1, p);
// return qpow::pow_normal(a, eulerFunction::SolveWithlogN(p) - 1, p);
}
ll exgcd(ll a, ll p)
{
return exgcd::inv(a, p);
}
void solve_normal(ll n, ll p, ll *ans)
{
ans[1] = 1;
for (ll i = 2; i <= n; ++i)
{
ans[i] = (-(p / i) * ans[p % i]) % p;
if (ans[i] < 0)
ans[i] += p;
}
}
void solve_fac(ll p, ll *fac, ll *facinv, ll *inv)
{
facinv[0] = fac[0] = 1;
for (ll i = 1; i < p; ++i)
fac[i] = fac[i - 1] * i % p;
facinv[p - 1] = EulerTheorem(fac[p - 1], p);
for (ll i = p - 2; i >= 1; --i)
facinv[i] = facinv[i + 1] * i % p;
for (ll i = 1; i < p; ++i)
inv[i] = facinv[i] * fac[i - 1] % p;
}
// O(n + logp) 离线求n个数在模p意义下的乘法逆元
void solve_special(int n, ll *a, ll *s, ll *invs, ll *inv, ll MOD)
{
s[0] = 1;
for (int i = 1; i <= n; ++i)
s[i] = (s[i - 1] * a[i]) % MOD;
invs[n] = qpow::pow_special(s[n], MOD - 2, MOD);
for (int i = n - 1; i >= 1; --i)
invs[i] = invs[i + 1] * a[i + 1] % MOD;
for (int i = 1; i <= n; ++i)
inv[i] = invs[i] * s[i - 1] % MOD;
}
} // namespace inv
namespace Möbius
{
const int N = 10000000;
int mu[N] = {0}, vis[N] = {0}, pri[N] = {0}, cnt = 0;
void get_mu(int n)
{
mu[1] = vis[1] = 1;
for (int i = 2; i <= n; ++i)
{
if (!vis[i])
pri[++cnt] = i,
mu[i] = -1;
for (int j = 1; j <= cnt && pri[j] * i <= n; ++j)
{
vis[i * pri[j]] = 1;
if (i % pri[j] == 0)
break;
mu[i * pri[j]] = -mu[i];
}
}
}
//f(n) = n / 1 + n / 2 + ... + n / n
int get_sum(int n)
{
int ans = 0;
for (int l = 1, r; l <= n; l = r + 1)
{
r = (n / (n / l));
ans += (r - l + 1) * (n / l);
}
return ans;
}
} // namespace Möbius
namespace sum
{
typedef long long LL;
const int maxn = 1700000;
int N;
LL s1[maxn + 100], s2[1300];
int vis[1300];
LL S(int n)
{
if (n <= maxn)
return s1[n];
int x = N / n;
if (vis[x])
return s2[x];
vis[x] = 1;
LL &ans = s2[x];
ans = (1 + n) * 1ll * n / 2;
for (int l = 2, r; l <= n; l = r + 1)
{
r = (n / (n / l));
ans -= (r - l + 1) * S(n / l);
}
return ans;
}
} // namespace sum
namespace FFT
{
const int MAXN = 500000;
struct comp
{
double x, y;
comp(double _x = 0, double _y = 0) : x(_x), y(_y) {}
} A[MAXN], B[MAXN], eps[MAXN], ieps[MAXN];
comp operator+(comp a, comp b)
{
return comp(a.x + b.x, a.y + b.y);
}
comp operator-(comp a, comp b)
{
return comp(a.x - b.x, a.y - b.y);
}
comp operator*(comp a, comp b)
{
return comp(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
const double pi = acos(-1);
void init(int len)
{
for (int i = 0, l; l = (1 << i), l <= len; ++i)
{
eps[i] = comp(cos(2 * pi / l), sin(2 * pi / l));
ieps[i] = comp(cos(2 * pi / l), -sin(2 * pi / l));
}
}
void FFT(comp *x, int len, comp *p)
{
for (int i = 0, j = 0; i < len; ++i)
{
if (i > j)
std::swap(x[i], x[j]);
for (int l = len >> 1; (j ^= l) < l; l >>= 1)
;
}
for (int i = 1, l; (l = 1 << i) <= len; ++i)
{
int mid = l >> 1;
for (int j = 0; j < len; j += l)
{
comp w0(1);
for (int k = j; k < j + mid; ++k)
{
comp t = w0 * x[k + mid];
x[k + mid] = x[k] - t;
x[k] = x[k] + t;
w0 = w0 * p[i];
}
}
}
}
int main()
{
int n, m;
init::rd(n, m);
for (int i = 0; i <= n; ++i)
init::rd(A[i].x);
for (int i = 0; i <= m; ++i)
init::rd(B[i].x);
int len = 1;
while (len <= n + m)
len <<= 1;
init(len);
FFT(A, len, eps);
FFT(B, len, eps);
for (int i = 0; i <= len; ++i)
A[i] = A[i] * B[i];
FFT(A, len, ieps);
for (int i = 0; i <= n + m; ++i)
printf("%d ", int(A[i].x / len + 0.5));
return 0;
}
} // namespace FFT
namespace linearBasis
{
// 线性基是竞赛中常用来解决子集异或一类题目的算法
typedef long long LL;
const int MAXL = 60;
int n;
LL a[MAXL + 5];
std::vector<LL> v;
void insert(LL t)
{
for (int j = MAXL; j >= 0; --j)
{
if (!(t & (1ll << j)))
continue;
if (a[j])
t ^= a[j];
else
{
for (int k = 0; k < j; ++k)
if (t & (1ll << k))
t ^= a[k];
for (int k = j + 1; k <= MAXL; ++k)
if (a[k] & (1ll << j))
a[k] ^= t;
a[j] = t;
return;
}
}
}
void move_into_vector()
{
v.clear();
for (int i = 0; i <= MAXL; ++i)
if (a[i])
v.push_back(a[i]);
}
void merge(LL *b)
{
for (int i = 0; i <= MAXL; ++i)
insert(b[i]);
}
LL query_MAX()
{
LL ans = 0;
for (int i = 0; i <= MAXL; ++i)
ans ^= a[i];
return ans;
}
// 询问第k小
LL query_kth(LL k)
{
LL ans = 0;
if ((int)v.size() != n)
--k;
if (k >= 1ll << v.size())
return -1;
for (size_t i = 0; i < v.size(); ++i)
if (k & (1ll << i))
ans ^= v[i];
return ans;
}
} // namespace linearBasis
namespace SORT
{
#define mid(l, r) (((l) + (r)) >> 1)
void bubbleSort(int *a, int n)
{
for (int i = 1; i < n; ++i)
for (int j = n - 1; j >= i; --j)
if (a[j] > a[j + 1])
std::swap(a[j], a[j + 1]);
}
void selectionSort(int *a, int n)
{
for (int i = 1; i < n; ++i)
for (int j = i + 1; j <= n; ++j)
if (a[i] > a[j])
std::swap(a[i], a[j]);
}
void insertSort(int *a, int n)
{
std::vector<int> v;
v.push_back(a[1]);
for (int i = 2; i <= n; ++i)
v.insert(std::lower_bound(v.begin(), v.end(), a[i]), a[i]);
for (int i = 1; i <= n; ++i)
a[i] = v[i - 1];
}
void mergeSort(int *a, int n, int l, int r)
{
if (l == r)
return;
int m = mid(l, r);
mergeSort(a, n, l, m);
mergeSort(a, n, m + 1, r);
std::inplace_merge(a + l, a + m + 1, a + r + 1);
// const int N = 100000;
// int b[N];
// int l1 = l, r1 = m + 1, l2 = m + 1, r2 = r + 1, p = l;
// while (l1 < r1 && l2 < r2)
// if (a[l1] <= a[l2])
// b[p++] = a[l1++];
// else
// b[p++] = a[l2++];
// while (l1 < r1)
// b[p++] = a[l1++];
// while (l2 < r2)
// b[p++] = a[l2++];
// for (int i = l; i <= r; ++i)
// a[i] = b[i];
}
void quickSort(int *a, int n, int l, int r)
{
int x = l, y = r, m = a[mid(l, r)];
do
{
while (a[l] < m)
++l;
while (a[r] > m)
--r;
if (l <= r)
std::swap(a[l++], a[r--]);
} while (l <= r);
if (l < y)
quickSort(a, n, l, y);
if (r > x)
quickSort(a, n, x, r);
}
#undef mid
} // namespace SORT
namespace suffixSort
{
const int MAXN = 2000000;
int tax[MAXN], tp[MAXN], rak[MAXN], sa[MAXN];
// N : 后缀个数 M : 字符集大小
void redixSort(int N, int M)
{
for (int i = 0; i <= M; ++i)
tax[i] = 0;
for (int i = 1; i <= N; ++i)
++tax[rak[i]];
for (int i = 1; i <= M; ++i)
tax[i] += tax[i - 1];
for (int i = N; i >= 1; --i)
sa[tax[rak[tp[i]]]--] = tp[i];
}
void suffixSort(char *ch, int len)
{
int M = 'z' - '0' + 1;
for (int i = 1; i <= len; ++i)
rak[i] = ch[i] - '0' + 1,
tp[i] = i;
redixSort(len, M);
int p = 0;
for (int w = 1; p < len; w <<= 1, M = p)
{
//这里的p仅为计数器
p = 0;
for (int i = 1; i <= w; ++i)
tp[++p] = len - w + i;
for (int i = 1; i <= len; ++i)
if (sa[i] > w)
tp[++p] = sa[i] - w;
redixSort(len, M);
std::swap(rak, tp); //此时tp为临时数组用于更新下次字符集和rak数组， 上一次的tp以被丢弃
rak[sa[1]] = 1;
//这里的p用于统计字符集大小
p = 1;
for (int i = 2; i <= len; ++i)
rak[sa[i]] = (tp[sa[i]] == tp[sa[i - 1]] && tp[sa[i] + w] == tp[sa[i - 1] + w]) ? p : ++p;
}
}
char ch[MAXN];
void run()
{
std::cin >> (ch + 1);
int len = strlen(ch + 1);
suffixSort(ch, len);
}
} // namespace suffixSort
namespace KMP
{
//数组从一开始储存哦 qwq
void kmp(char *s1, char *s2, int l1, int l2, int *nxt, int *ans, int &cnt)
{
cnt = 0;
nxt[1] = 0;
for (int i = 2; i <= l2; ++i)
{
int p = nxt[i - 1];
while (s2[p + 1] != s2[i] && p)
p = nxt[p];
nxt[i] = s2[p + 1] == s2[i] ? p + 1 : 0;
}
int j = 0;
for (int i = 1; i <= l1; ++i)
{
while (j && s1[i] != s2[j + 1])
j = nxt[j];
if (s1[i] == s2[j + 1])
++j;
if (j == l2)
ans[++cnt] = j,
j = nxt[j];
}
}
} // namespace KMP
namespace manacher
{
const int N = 41000000;
void init(char *ch1, char *ch2, int len1, int &len2)
{
len2 = 1;
ch2[0] = '$';
ch2[1] = '#';
for (int i = 0; i < len1; ++i)
{
ch2[++len2] = ch1[i];
ch2[++len2] = '#';
}
}
int manachar(char *ch, int len)
{
int l[N] = {0}, id = 0, md = 0, ans = 0;
for (int i = 1; i <= len; ++i)
{
if (md > i)
l[i] = min(md - i, l[id * 2 - i]);
else
l[i] = 1;
while (ch[i - l[i]] == ch[i + l[i]])
++l[i];
if (i + l[i] > md)
md = i + l[i],
id = i;
}
for (int i = 1; i <= len; ++i)
ans = max(ans, l[i]);
return ans - 1;
}
} // namespace manacher
namespace trie
{
const int N = 100000;
struct node
{
int son[100];
int val;
int x;
int fail;
node()
{
for (int i = 0; i < 100; ++i)
son[i] = 0;
val = x = fail = 0;
}
} trie[N];
int head[N], nxt[N], val[N];
int x[N];
int root;
int cnt;
void add_normal(char *ch, int len)
{
int o = root;
for (int i = 0; i < len; ++i)
{
if (trie[o].son[ch[i] - '0'])
{
o = trie[o].son[ch[i] - '0'];
}
else
{
trie[o].son[ch[i] - '0'] = ++cnt;
o = cnt;
}
}
++trie[o].x;
}
void add_special(char *ch, int len)
{
int o = root;
for (int i = 0; i < len; ++i)
{
int p = 0;
for (int j = head[o]; j; j = nxt[j])
if (val[j] == ch[i])
p = j;
if (p)
o = p;
else
{
nxt[++cnt] = head[o];
head[o] = cnt;
val[cnt] = ch[i];
o = cnt;
}
}
++x[o];
}
void get_fail()
{
const int M = N << 4;
int qu[M + 2], l, r;
l = r = 0;
for (int i = '0' - '0'; i <= 'z' - '0'; ++i)
if (trie[root].son[i])
qu[r++] = trie[root].son[i];
while (l != r)
{
int p = qu[l++];
int t = trie[p].fail;
if (l > M)
l = 0;
for (int i = '0' - '0'; i <= 'z' - '0'; ++i)
if (trie[p].son[i])
{
qu[r++] = trie[p].son[i];
if (r > M)
r = 0;
trie[trie[p].son[i]].fail = trie[t].son[i];
}
else
{
trie[p].son[i] = trie[t].son[i];
}
}
}
int Aho_Corasick_Automaton(char *ch, int len)
{
int ans = 0;
int o = root;
for (int i = 0; i < len; ++i)
{
o = trie[o].son[ch[i] - '0'];
for (int j = o; j && ~trie[j].x; j = trie[j].fail)
ans += trie[j].x,
trie[j].x = -1;
}
return ans;
}
} // namespace trie
namespace CG
{
#define sqr(x) ((x) * (x))
struct point
{
double x, y;
};
struct segment
{
point l, r;
};
inline double dis(point a, point b)
{
return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));
}
struct circle
{
point cen;
double r;
};
typedef std::vector<point> polygon;
inline point make_vec(point a, point b)
{
point x;
x.x = b.x - a.x;
x.y = b.y - a.y;
return x;
}
//点积 a ⊥ b时点积为0
inline double dot(point a, point b)
{
return a.x * b.x + a.y * b.y;
}
// 叉积 a ∥ b时叉积为0，b在a逆时针为正，否则为负
// 几何意义是四边形不等式面积
inline double cro(point a, point b)
{
return a.x * b.y - a.y * b.x;
}
// 求多边形面积
// 逆时针储存
inline double area(polygon &a)
{
double ans = cro(a[a.size()], a[0]);
for (std::size_t i = 0; i < a.size(); ++i)
{
ans += cro(a[i], a[i + 1]);
}
return ans / 2;
}
// 旋转
inline void turn(point &a, double b)
{
point t = a;
a.x = t.x * cos(b) - t.y * sin(b);
a.y = t.x * sin(b) - t.y * cos(b);
}
// 判断点是否在直线上
inline bool on_line(point a, segment b)
{
return cro(make_vec(a, b.l), make_vec(a, b.r)) == 0;
}
// 判断点是否在线段上
inline bool on_segment(point a, segment b)
{
return dis(a, b.l) + dis(a, b.r) == dis(b.l, b.r);
}
// 海伦公式
inline double heron(double a, double b, double c)
{
double p = (a + b + c) / 2;
return sqrt(p * (p - a) * (p - b) * (p - c));
}
#undef sqr
} // namespace CG
namespace maximumFlow
{
typedef long long LL;
const int MAX = 30000;
int n;
int cnt = 1;
int head[MAX], nxt[MAX], to[MAX], cap[MAX], flow[MAX];
int dis[MAX], cur[MAX];
int qu[(MAX << 1) + 2], ql, qr;
void insert(int u, int v, int f)
{
nxt[++cnt] = head[u];
to[cnt] = v;
cap[cnt] = f;
flow[cnt] = 0;
head[u] = cnt;
}
bool bfs(int s, int t)
{
for (int i = 1; i <= n; ++i)
dis[i] = 0,
cur[i] = head[i];
ql = qr = 0;
qu[qr++] = s;
dis[s] = 1;
while (ql != qr)
{
int now = qu[ql++];
if (ql > MAX << 1)
ql = 0;
for (int i = head[now], v = to[i]; i; i = nxt[i], v = to[i])
if (cap[i] > flow[i] && !dis[v])
{
dis[v] = dis[now] + 1;
if (v == t)
return true;
qu[qr++] = v;
if (qr > MAX << 1)
qr = 0;
}
}
return false;
}
int dfs(int u, int maxflow, int t)
{
if (u == t)
return maxflow;
int ans = 0, temp;
for (int &i = cur[u], v = to[i]; i; i = nxt[i], v = to[i])
{
if (cap[i] > flow[i] && dis[v] == dis[u] + 1)
{
temp = dfs(v, min(maxflow - ans, cap[i] - flow[i]), t);
flow[i] += temp;
flow[i ^ 1] -= temp;
ans += temp;
if (ans >= maxflow)
break;
}
}
if (!ans)
dis[u] = -2;
return ans;
}
LL dinic(int s, int t)
{
LL ans = 0;
while (bfs(s, t))
ans += dfs(s, 0x3fffffff, t);
return ans;
}
// 无源汇有上下界可行流
int d[MAX], k[MAX];
int main1()
{
int m, u, v, lower, upper, s, t;
init::rd(n, m);
for (int i = 1; i <= m; ++i)
{
init::rd(u, v, lower, upper);
d[i] = lower;
k[u] -= lower;
k[v] += lower;
insert(u, v, upper - lower);
insert(v, u, 0);
}
s = n + 1;
t = n + 2;
int sum = 0;
for (int i = 1; i <= n; ++i)
{
if (k[i] < 0)
insert(i, t, -k[i]),
insert(t, i, 0);
else
insert(s, i, k[i]),
insert(i, s, 0),
sum += k[i];
}
n += 2;
if (dinic(s, t) != sum)
printf("NO\n");
else
printf("YES\n");
return 0;
}
// 有源汇有上下界最大流
int main2()
{
int m, u, v, lower, upper, s, t, ss, tt;
init::rd(n, m, s, t);
for (int i = 1; i <= m; ++i)
{
init::rd(u, v, lower, upper);
d[i] = lower;
k[u] -= lower;
k[v] += lower;
insert(u, v, upper - lower);
insert(v, u, 0);
}
ss = n + 1;
tt = n + 2;
int sum = 0;
for (int i = 1; i <= n; ++i)
{
if (k[i] < 0)
insert(i, tt, -k[i]),
insert(tt, i, 0);
else
insert(ss, i, k[i]),
insert(i, ss, 0),
sum += k[i];
}
insert(t, s, 0x3fffffff);
insert(s, t, 0);
n += 2;
if (dinic(ss, tt) != sum)
printf("please go home to sleep\n");
else
printf("%d\n", dinic(s, t));
return 0;
}
// 有源汇有上下界最小流
int main3()
{
int m, u, v, lower, upper, s, t, ss, tt;
init::rd(n, m, s, t);
for (int i = 1; i <= m; ++i)
{
init::rd(u, v, lower, upper);
d[i] = lower;
k[u] -= lower;
k[v] += lower;
insert(u, v, upper - lower);
insert(v, u, 0);
}
ss = n + 1;
tt = n + 2;
int sum = 0;
for (int i = 1; i <= n; ++i)
{
if (k[i] < 0)
insert(i, tt, -k[i]),
insert(tt, i, 0);
else
insert(ss, i, k[i]),
insert(i, ss, 0),
sum += k[i];
}
n += 2;
int f = dinic(ss, tt);
insert(t, s, 0x3fffffff);
int p = cnt;
insert(s, t, 0);
f += dinic(ss, tt);
if (f != sum)
printf("please go home to sleep\n");
else
printf("%d\n", flow[p]);
return 0;
}
} // namespace maximumFlow
int main()
{
}
