#include <bits/stdc++.h>
using namespace std;

const int64_t MOD = 1e9+7;;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}
void mul(int64_t& a, int64_t b){
    a = a*b % MOD;
}

int64_t power_mod(int64_t num, int64_t power){
    int64_t prod = 1;
    num %= MOD;
    while(power > 0){
        if(power&1) prod = prod * num % MOD;
        num = num * num % MOD;
        power >>= 1;
    }
    return prod;
}

int main(){
    int N, K;
    cin >> N >> K;
    int64_t ans = N*K*(K+1)/2 * power_mod(K+1, N-1) % MOD;

    static int64_t dp[101][101*101];
    dp[N][0] = 1;
    int mx = 0;
    for(int i=N; i>0; i--){
        int mx2 = mx;
        for(int j=0; j<=mx; j++) for(int k=0; k<=K; k++){
            int op = 0;
            if(k <= i) op = (j+k) / i;
            int64_t sub = op * dp[i][j] % MOD * power_mod(K+1, i-1) % MOD;
            add(ans, MOD - sub);
            add(dp[i-1][j+op], dp[i][j]);
            mx2 = max(mx2, j+op);
        }
        mx = mx2;
    }
    cout << ans << endl;
    return 0;
}

### Prompt

In cpp, your task is to solve 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;

const int64_t MOD = 1e9+7;;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}
void mul(int64_t& a, int64_t b){
    a = a*b % MOD;
}

int64_t power_mod(int64_t num, int64_t power){
    int64_t prod = 1;
    num %= MOD;
    while(power > 0){
        if(power&1) prod = prod * num % MOD;
        num = num * num % MOD;
        power >>= 1;
    }
    return prod;
}

int main(){
    int N, K;
    cin >> N >> K;
    int64_t ans = N*K*(K+1)/2 * power_mod(K+1, N-1) % MOD;

    static int64_t dp[101][101*101];
    dp[N][0] = 1;
    int mx = 0;
    for(int i=N; i>0; i--){
        int mx2 = mx;
        for(int j=0; j<=mx; j++) for(int k=0; k<=K; k++){
            int op = 0;
            if(k <= i) op = (j+k) / i;
            int64_t sub = op * dp[i][j] % MOD * power_mod(K+1, i-1) % MOD;
            add(ans, MOD - sub);
            add(dp[i-1][j+op], dp[i][j]);
            mx2 = max(mx2, j+op);
        }
        mx = mx2;
    }
    cout << ans << endl;
    return 0;
}

```