#include <iostream>
#include <cmath>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <queue>
using namespace std;
int dp[110][11000],n,K,w[110];
const int mo=1e9+7;
int main(){
	scanf("%d%d",&n,&K);
	dp[n+1][0]=1; w[0]=1;
	for (int i=1;i<=n;i++) w[i]=1ll*w[i-1]*(K+1)%mo;
	int ans=1ll*n*K*(K+1)/2%mo;
	for (int i=1;i<=n-1;i++) ans=1ll*ans*(K+1)%mo;
	//cout<<ans<<endl;
	for (int i=n;i;i--)
		for (int j=0;j<=K;j++)
			for (int k=0;k<=n*n;k++)
				if (dp[i+1][k]){
					int num=(j+k)/i;
					if (j>i) num=0;
				//	cout<<i+1<<" "<<k<<" "<<dp[i+1][k]<<" "<<num<<endl;
					dp[i][k+num]=(dp[i][k+num]+dp[i+1][k])%mo;
					ans=(ans-1ll*w[i-1]*dp[i+1][k]%mo*num)%mo;
				}
	ans=(ans+mo)%mo;
	cout<<ans<<endl;
}
### Prompt

Please create a solution in Cpp to the following problem:

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 <iostream>
#include <cmath>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <queue>
using namespace std;
int dp[110][11000],n,K,w[110];
const int mo=1e9+7;
int main(){
	scanf("%d%d",&n,&K);
	dp[n+1][0]=1; w[0]=1;
	for (int i=1;i<=n;i++) w[i]=1ll*w[i-1]*(K+1)%mo;
	int ans=1ll*n*K*(K+1)/2%mo;
	for (int i=1;i<=n-1;i++) ans=1ll*ans*(K+1)%mo;
	//cout<<ans<<endl;
	for (int i=n;i;i--)
		for (int j=0;j<=K;j++)
			for (int k=0;k<=n*n;k++)
				if (dp[i+1][k]){
					int num=(j+k)/i;
					if (j>i) num=0;
				//	cout<<i+1<<" "<<k<<" "<<dp[i+1][k]<<" "<<num<<endl;
					dp[i][k+num]=(dp[i][k+num]+dp[i+1][k])%mo;
					ans=(ans-1ll*w[i-1]*dp[i+1][k]%mo*num)%mo;
				}
	ans=(ans+mo)%mo;
	cout<<ans<<endl;
}
```