#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=305,mod=1e9+7;
ll dp[N][N*N],sum[N][N*N];
int n,k;
int main()
{
    scanf("%d%d",&n,&k);
    dp[n+1][0]=1;
    int mx=0;
    for(int i=n+1;i>1;i--)
    {
        int t=mx;
        for(int j=0;j<=t;j++)
        {
            if(!dp[i][j]&&!sum[i][j]) continue;
            for(int h=0;h<=k;h++)
            {
                if(h<=i-1)
                {
                    mx=max(mx,j+(h+j)/(i-1));
                    int s=j+(h+j)/(i-1);
                    dp[i-1][s]=(dp[i-1][s]+dp[i][j])%mod;
                    sum[i-1][s]=(sum[i-1][s]+sum[i][j]+(h+j)%(i-1)*dp[i][j])%mod;
                }
                else
                {
                    dp[i-1][j]=(dp[i-1][j]+dp[i][j])%mod;
                    sum[i-1][j]=(sum[i-1][j]+sum[i][j]+(h+j)*dp[i][j]%mod)%mod;
                }
            }
        }
    }
    ll ans=0;
    for(int j=0;j<=mx;j++)
        ans=(ans+sum[1][j])%mod;
    printf("%lld\n",ans);
}

### 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
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=305,mod=1e9+7;
ll dp[N][N*N],sum[N][N*N];
int n,k;
int main()
{
    scanf("%d%d",&n,&k);
    dp[n+1][0]=1;
    int mx=0;
    for(int i=n+1;i>1;i--)
    {
        int t=mx;
        for(int j=0;j<=t;j++)
        {
            if(!dp[i][j]&&!sum[i][j]) continue;
            for(int h=0;h<=k;h++)
            {
                if(h<=i-1)
                {
                    mx=max(mx,j+(h+j)/(i-1));
                    int s=j+(h+j)/(i-1);
                    dp[i-1][s]=(dp[i-1][s]+dp[i][j])%mod;
                    sum[i-1][s]=(sum[i-1][s]+sum[i][j]+(h+j)%(i-1)*dp[i][j])%mod;
                }
                else
                {
                    dp[i-1][j]=(dp[i-1][j]+dp[i][j])%mod;
                    sum[i-1][j]=(sum[i-1][j]+sum[i][j]+(h+j)*dp[i][j]%mod)%mod;
                }
            }
        }
    }
    ll ans=0;
    for(int j=0;j<=mx;j++)
        ans=(ans+sum[1][j])%mod;
    printf("%lld\n",ans);
}

```