#include<bits/stdc++.h>

using namespace std;

const int mod = 1e9 + 7, N = 105;
int n, K, suma, dp[N][N * N], sumt;

int binpw (int aa, int mm) {
    int ret = 1;
    for (; mm; mm >>= 1, aa = (1LL * aa * aa) % mod) if(mm & 1) ret = (1LL * ret * aa) % mod;
    return ret;
}

int main () {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    cin >> n >> K;
    suma = (1LL * ( (K * (K + 1) ) / 2 * n) % mod * binpw(K + 1, n - 1) ) % mod;

    dp[n + 1][0] = 1;
    for (int i = n; i > 0; --i) {
        for (int j = 0; j < N * N; ++j) {
            if(!dp[i + 1][j]) continue;

            for (int k = 0; k <= K; ++k) {
                if(k <= i && j + (j + k) / i < N * N) {
                    dp[i][j + (j + k) / i] += dp[i + 1][j];
                    dp[i][j + (j + k) / i] %= mod;
                }
                if(k > i) {
                    dp[i][j] = (dp[i][j] + dp[i + 1][j]) % mod;
                }
            }
        }
    }

    for (int i = 0; i < N * N; ++i) sumt = (sumt + 1LL * i * dp[1][i]) % mod;

    cout << (suma - sumt + mod) % mod;

    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 int mod = 1e9 + 7, N = 105;
int n, K, suma, dp[N][N * N], sumt;

int binpw (int aa, int mm) {
    int ret = 1;
    for (; mm; mm >>= 1, aa = (1LL * aa * aa) % mod) if(mm & 1) ret = (1LL * ret * aa) % mod;
    return ret;
}

int main () {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    cin >> n >> K;
    suma = (1LL * ( (K * (K + 1) ) / 2 * n) % mod * binpw(K + 1, n - 1) ) % mod;

    dp[n + 1][0] = 1;
    for (int i = n; i > 0; --i) {
        for (int j = 0; j < N * N; ++j) {
            if(!dp[i + 1][j]) continue;

            for (int k = 0; k <= K; ++k) {
                if(k <= i && j + (j + k) / i < N * N) {
                    dp[i][j + (j + k) / i] += dp[i + 1][j];
                    dp[i][j + (j + k) / i] %= mod;
                }
                if(k > i) {
                    dp[i][j] = (dp[i][j] + dp[i + 1][j]) % mod;
                }
            }
        }
    }

    for (int i = 0; i < N * N; ++i) sumt = (sumt + 1LL * i * dp[1][i]) % mod;

    cout << (suma - sumt + mod) % mod;

    return 0;
}

```