Codeforces Round #210 (Div. 1) B 二分+dp

B. Levko and Array

 

standard output

Levko has an array that consists of integers: a1, a2, ... , an. But he doesn’t like this array at all.

Levko thinks that the beauty of the array a directly depends on value c(a), which can be calculated by the formula:

The less value c(a) is, the more beautiful the array is.

It’s time to change the world and Levko is going to change his array for the better. To be exact, Levko wants to change the values of at most k array elements (it is allowed to replace the values by any integers). Of course, the changes should make the array as beautiful as possible.

Help Levko and calculate what minimum number c(a) he can reach.

Input

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 2000). The second line contains space-separated integers a1, a2, ... , an( - 109 ≤ ai ≤ 109).

Output

A single number — the minimum value of c(a) Levko can get.

Examples

input

Copy

5 2
4 7 4 7 4

output

Copy

0

input

Copy

3 1
-100 0 100

output

Copy

100

input

Copy

6 3
1 2 3 7 8 9

output

Copy

1

Note

In the first sample Levko can change the second and fourth elements and get array: 4, 4, 4, 4, 4.

In the third sample he can get array: 1, 2, 3, 4, 5, 6.

 

二分+DP问题

ok(x) 表示max(abs(a[i]-a[i+1])) = x 时修改的次数是否小于等于K

ans[i] 表示前i个数最少修改多少使的相差小于x
当a[i]-a[j] <= x(i-j)时 表示可以不修改第i个和第j个，修改j-i中间的数就能使的
相差小于x了。

#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int N = 2020;
ll a[N], ans[N];
ll n, k;
bool ok(ll x) {
    ll res = N;
    for(ll i = 1; i <= n; i ++) {
        ans[i] = i-1;
        for(ll j = 1; j < i; j ++) {
            if(abs(a[i]-a[j]) <= x*(i-j))
                ans[i] = min(ans[i], ans[j]+i-j-1);
        }
        res = min(res,ans[i]+n-i);
    }
    return res <= k;
}
int main() {
    cin >> n >> k;
    for(int i = 1; i <= n; i ++) cin >> a[i];
    ll l = 0, r = 2e9;
    while(l < r) {
        ll m = (l+r) >> 1;
        if(ok(m)) r = m;
        else l = m+1;
    }
    printf("%lld\n",r);
    return 0;
}