#include <bits/stdc++.h>
using namespace  std;
typedef long long ll;
const int N = 110;
const int P = 1e9+7;
int f[N][N*N],n,k;

inline void add(int &x,int y){
	x=(x+y)%P;
}

int main(){
	scanf("%d%d",&n,&k);
	int ans = 1;
	for(int i = 1;i<n;i++) ans = 1ll*ans*(k+1)%P;
	ans = 1ll*ans*((1+k)*k/2)%P*n%P;
	f[n+1][0] =1;
	int up;
	//cout<<ans<<endl;
	for(int i = n;i>0;i--){
		up = (n-i)*k;
	//	cout<<up<<endl;
		for(int j = 0;j<=k;j++){
			if(j<=i)
				for(int w = 0;w<=up;w++){
					add(f[i][w+(w+j)/i],f[i+1][w]);
				}
			else 
				for(int w = 0;w<=up;w++){
					add(f[i][w],f[i+1][w]);
				}
			// f[i][   w + (w+j)/j]
		}
	}
	//cout<<f[2][0]<<' '<<f[2][1]<<' '<<f[2][2]<<endl;
	//cout<<f[1][0]<<' '<<f[1][1]<<' '<<f[1][2]<<' '<<f[1][3]<<' '<<f[1][4]<<endl;
	for(int i = 0;i<=n*k;i++) add(ans,-1ll*f[1][i]*i%P);
	ans = (ans+P)%P;
	printf("%d\n",ans);
	return 0;
}
### 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 <bits/stdc++.h>
using namespace  std;
typedef long long ll;
const int N = 110;
const int P = 1e9+7;
int f[N][N*N],n,k;

inline void add(int &x,int y){
	x=(x+y)%P;
}

int main(){
	scanf("%d%d",&n,&k);
	int ans = 1;
	for(int i = 1;i<n;i++) ans = 1ll*ans*(k+1)%P;
	ans = 1ll*ans*((1+k)*k/2)%P*n%P;
	f[n+1][0] =1;
	int up;
	//cout<<ans<<endl;
	for(int i = n;i>0;i--){
		up = (n-i)*k;
	//	cout<<up<<endl;
		for(int j = 0;j<=k;j++){
			if(j<=i)
				for(int w = 0;w<=up;w++){
					add(f[i][w+(w+j)/i],f[i+1][w]);
				}
			else 
				for(int w = 0;w<=up;w++){
					add(f[i][w],f[i+1][w]);
				}
			// f[i][   w + (w+j)/j]
		}
	}
	//cout<<f[2][0]<<' '<<f[2][1]<<' '<<f[2][2]<<endl;
	//cout<<f[1][0]<<' '<<f[1][1]<<' '<<f[1][2]<<' '<<f[1][3]<<' '<<f[1][4]<<endl;
	for(int i = 0;i<=n*k;i++) add(ans,-1ll*f[1][i]*i%P);
	ans = (ans+P)%P;
	printf("%d\n",ans);
	return 0;
}
```