#include<bits/stdc++.h>
const int N = 105;
const int mod = 1e9 + 7;
using namespace std;

int n, k, f[N][N*N], ans;

void add(int&a, int b){
    a += b; if (a >= mod) a -= mod; if (a < 0) a += mod;
}

int main(){
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    cin >> n >> k;
    f[n+1][0] = 1;
    int cnt = 0;
    ans = 1LL * k * (k+1) / 2 % mod;
    for (int i = 2; i <= n; i++) ans = 1LL * ans * (k+1) % mod;
    ans = 1LL * ans * n % mod;
    for (int i = n; i >= 1; i--) {
        int cur = cnt;
        cnt += (cnt + min(i, k)) / i;
        for (int j = 0; j <= cnt; j++){
            for (int l = min(cur, j); l >= 0; l--){
                int Min = max((j - l) * i - l, 0), Max = min(min(k, i), (j-l+1)*i-1-l);
                if (l == j){
                    if (k > i) add(f[i][j], 1LL * f[i+1][j] * (k-i) % mod);
                }
                if (Max < Min) continue;
                add(f[i][j], 1LL * f[i+1][l] * (Max - Min + 1) % mod);
            }
        }
    }
    for (int i = 0; i <= cnt; i++){
        add(ans, -1LL * f[1][i] * i % mod);
    }
    cout << ans << endl;
}

### 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>
const int N = 105;
const int mod = 1e9 + 7;
using namespace std;

int n, k, f[N][N*N], ans;

void add(int&a, int b){
    a += b; if (a >= mod) a -= mod; if (a < 0) a += mod;
}

int main(){
    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    cin >> n >> k;
    f[n+1][0] = 1;
    int cnt = 0;
    ans = 1LL * k * (k+1) / 2 % mod;
    for (int i = 2; i <= n; i++) ans = 1LL * ans * (k+1) % mod;
    ans = 1LL * ans * n % mod;
    for (int i = n; i >= 1; i--) {
        int cur = cnt;
        cnt += (cnt + min(i, k)) / i;
        for (int j = 0; j <= cnt; j++){
            for (int l = min(cur, j); l >= 0; l--){
                int Min = max((j - l) * i - l, 0), Max = min(min(k, i), (j-l+1)*i-1-l);
                if (l == j){
                    if (k > i) add(f[i][j], 1LL * f[i+1][j] * (k-i) % mod);
                }
                if (Max < Min) continue;
                add(f[i][j], 1LL * f[i+1][l] * (Max - Min + 1) % mod);
            }
        }
    }
    for (int i = 0; i <= cnt; i++){
        add(ans, -1LL * f[1][i] * i % mod);
    }
    cout << ans << endl;
}

```