/*********************
*  Author: xuziyuan  * 
*********************/

#include <bits/stdc++.h>

#define rt0 return 0
#define rep(i,n) for(int i=0;i<n;i++)
#define repn(i,n) for(int i=1;i<=n;i++)
#define replet(c) for(char c='a';c<='z';c++) 
#define LL long long
#define pii pair <int,int>
#define pb push_back
#define fi first
#define se second
#define mpr make_pair
#define sqr(a) ((a)*(a))

using namespace std;

const LL MOD=1e9+7;

LL n,t,dp[110][10010],all=1,ans=0;

int main()
{
	cin>>n>>t;
	rep(i,n-1) all=all*(t+1)%MOD;
	all=all*(t+1)*t/2*n%MOD;
	dp[n][0]=1;
	for(int i=n;i>0;i--)
	{
		rep(j,10005)
		{
			rep(k,t+1)
			{
				if(dp[i][j]==0) continue;
				if(k<=i) dp[i-1][j+(j+k)/i]=(dp[i-1][j+(j+k)/i]+dp[i][j])%MOD;
				else dp[i-1][j]=(dp[i-1][j]+dp[i][j])%MOD;
			}
		}
	}
	repn(i,10003) ans=(ans+i*dp[0][i])%MOD;
	cout<<(all-ans+MOD)%MOD<<endl;
	rt0;
}
### Prompt

Please formulate a cpp solution 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
/*********************
*  Author: xuziyuan  * 
*********************/

#include <bits/stdc++.h>

#define rt0 return 0
#define rep(i,n) for(int i=0;i<n;i++)
#define repn(i,n) for(int i=1;i<=n;i++)
#define replet(c) for(char c='a';c<='z';c++) 
#define LL long long
#define pii pair <int,int>
#define pb push_back
#define fi first
#define se second
#define mpr make_pair
#define sqr(a) ((a)*(a))

using namespace std;

const LL MOD=1e9+7;

LL n,t,dp[110][10010],all=1,ans=0;

int main()
{
	cin>>n>>t;
	rep(i,n-1) all=all*(t+1)%MOD;
	all=all*(t+1)*t/2*n%MOD;
	dp[n][0]=1;
	for(int i=n;i>0;i--)
	{
		rep(j,10005)
		{
			rep(k,t+1)
			{
				if(dp[i][j]==0) continue;
				if(k<=i) dp[i-1][j+(j+k)/i]=(dp[i-1][j+(j+k)/i]+dp[i][j])%MOD;
				else dp[i-1][j]=(dp[i-1][j]+dp[i][j])%MOD;
			}
		}
	}
	repn(i,10003) ans=(ans+i*dp[0][i])%MOD;
	cout<<(all-ans+MOD)%MOD<<endl;
	rt0;
}
```