#include <algorithm>
#include <cstdio>
#include <iostream>
#include <cfloat>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <queue>
#include <sstream>
#include <stack>
#include <time.h>
#include <vector>
#include <complex>
#include <map>
#include <set>
#include <iomanip>
#include <math.h>
#include <stdlib.h>
#include <list>
#include <utility>
#include <memory>
#include <cstring>
#include <fstream>
#include <numeric>
#include <assert.h>
#include <bitset>
#include <ios> 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n,m; 
const int mod=1e9+7;
const ll MOD=1e9+7;
int dp[103][10004];
int main(){
	ll a=1;
	cin>>n>>m;
	for (int i=0;i<n-1;i++) a=a*(m+1)%MOD;
	dp[n+1][0]=1;
	for (int i=n;i>=1;i--)
		for (int j=0;j<=m;j++)
			for (int k=0;k<=10000;k++){	
				if (j>i){
					dp[i][k]=(dp[i+1][k]+dp[i][k])%mod;
					continue;
				}
				int x=(j+k)/i;
				if (x+k>10000) continue;
				dp[i][x+k]=(dp[i+1][k]+dp[i][x+k])%mod;
			}
	ll res=a*m*(m+1)/2*n%MOD;
	for (int i=0;i<=10000;i++)
		res=(res-1ll*dp[1][i]*i+MOD)%MOD;
	cout<<res;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

Consider the following game:

* The game is played using a row of N squares and many stones.
* First, a_i stones are put in Square i\ (1 \leq i \leq N).
* A player can perform the following operation as many time as desired: "Select an integer i such that Square i contains exactly i stones. Remove all the stones from Square i, and add one stone to each of the i-1 squares from Square 1 to Square i-1."
* The final score of the player is the total number of the stones remaining in the squares.



For a sequence a of length N, let f(a) be the minimum score that can be obtained when the game is played on a.

Find the sum of f(a) over all sequences a of length N where each element is between 0 and K (inclusive). Since it can be extremely large, find the answer modulo 1000000007 (= 10^9+7).

Constraints

* 1 \leq N \leq 100
* 1 \leq K \leq N

Input

Input is given from Standard Input in the following format:


N K


Output

Print the sum of f(a) modulo 1000000007 (= 10^9+7).

Examples

Input

2 2


Output

10


Input

20 17


Output

983853488

### Response

```cpp
#include <algorithm>
#include <cstdio>
#include <iostream>
#include <cfloat>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <queue>
#include <sstream>
#include <stack>
#include <time.h>
#include <vector>
#include <complex>
#include <map>
#include <set>
#include <iomanip>
#include <math.h>
#include <stdlib.h>
#include <list>
#include <utility>
#include <memory>
#include <cstring>
#include <fstream>
#include <numeric>
#include <assert.h>
#include <bitset>
#include <ios> 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n,m; 
const int mod=1e9+7;
const ll MOD=1e9+7;
int dp[103][10004];
int main(){
	ll a=1;
	cin>>n>>m;
	for (int i=0;i<n-1;i++) a=a*(m+1)%MOD;
	dp[n+1][0]=1;
	for (int i=n;i>=1;i--)
		for (int j=0;j<=m;j++)
			for (int k=0;k<=10000;k++){	
				if (j>i){
					dp[i][k]=(dp[i+1][k]+dp[i][k])%mod;
					continue;
				}
				int x=(j+k)/i;
				if (x+k>10000) continue;
				dp[i][x+k]=(dp[i+1][k]+dp[i][x+k])%mod;
			}
	ll res=a*m*(m+1)/2*n%MOD;
	for (int i=0;i<=10000;i++)
		res=(res-1ll*dp[1][i]*i+MOD)%MOD;
	cout<<res;
}
```