BJOJ 4402 Claris的剑 (组合数学，思维)

题目：传送门

题意

 

思路

大佬精讲

#include <bits/stdc++.h>
#define LL long long
#define ULL unsigned long long
#define UI unsigned int
#define mem(i, j) memset(i, j, sizeof(i))
#define rep(i, j, k) for(int i = j; i <= k; i++)
#define dep(i, j, k) for(int i = k; i >= j; i--)
#define pb push_back
#define make make_pair
#define INF 0x3f3f3f3f
#define inf LLONG_MAX
#define PI acos(-1)
#define fir first
#define sec second
#define lb(x) ((x) & (-(x)))
#define dbg(x) cout<<#x<<" = "<<x<<endl;
using namespace std;

const int N = 1e7 + 5;

const LL mod = 1e9 + 7;

LL fac[N], ifac[N];

LL ksm(LL a, LL b) {

    LL res = 1LL;

    while(b) {

        if(b & 1) res = res * a % mod;

        a = a * a % mod; b >>= 1;

    }

    return res;

}

LL C(int n, int m) {

    return fac[n] * ifac[m] % mod * ifac[n - m] % mod;

}

int n, m;

void solve() {

    scanf("%d %d", &n, &m);

    fac[0] = ifac[0] = 1LL;

    rep(i, 1, n) fac[i] = 1LL * i * fac[i - 1] % mod;

    ifac[n] = ksm(fac[n], mod - 2);

    dep(i, 1, n - 1) ifac[i] = 1LL * (i + 1) * ifac[i + 1] % mod;

    LL ans = 1LL;

    rep(i, 0, min(m - 2, n - 2)) {

        ans = (ans + C(((n - i - 2) / 2) + i + 1, i + 1)) % mod;

    }

    rep(i, 0, min(m - 2, n - 3)) {

        ans = (ans + C(((n - i - 3) / 2) + i + 1, i + 1)) % mod;

    }

    printf("%lld\n", ans);

}


int main() {

//    int _; scanf("%d", &_);
//    while(_--) solve();

    solve();

    return 0;
}