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

const int mod = 1000*1000*1000+7;
int N, K;
int po[102];

int cc[102][10010];
int dp(int idx, int cnt) {
    int &ret = cc[idx][cnt];
    if(ret != -1) return ret;
    if(idx == 0) return ret = 0;

    ret = 0;
    for(int i = 0; idx * i - cnt <= K; i++) {
        int st = max(0, idx * i - cnt);
        int ed = min(idx, min(K + 1, idx * (i + 1) - cnt) - 1);

        if(st > ed) continue;

        ret += 1LL * dp(idx - 1, cnt + i) * (ed - st + 1) % mod;
        ret %= mod;
        ret += 1LL * (mod - i) * (ed - st + 1) % mod * po[idx - 1] % mod;
        ret %= mod;
        ret += 1LL * (st + ed) * (ed - st + 1) / 2 % mod * po[idx - 1] % mod;
        ret %= mod;
    }
    //*
    if(idx + 1 <= K) {
        ret += 1LL * dp(idx - 1, cnt) * (K - idx) % mod;
        ret %= mod;
        ret += 1LL * (idx + 1 + K) * (K - idx) / 2 % mod * po[idx - 1] % mod;
        ret %= mod;
    }
    //*/
    return ret;
}

int main() {
    scanf("%d %d", &N, &K);

    po[0] = 1;
    for(int i = 1; i < 102; i++) {
        po[i] = 1LL * po[i - 1] * (K + 1) % mod;
    }

    memset(cc, -1, sizeof(cc));
    printf("%d", dp(N, 0));
}

### Prompt

Please create a solution in cpp 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;

const int mod = 1000*1000*1000+7;
int N, K;
int po[102];

int cc[102][10010];
int dp(int idx, int cnt) {
    int &ret = cc[idx][cnt];
    if(ret != -1) return ret;
    if(idx == 0) return ret = 0;

    ret = 0;
    for(int i = 0; idx * i - cnt <= K; i++) {
        int st = max(0, idx * i - cnt);
        int ed = min(idx, min(K + 1, idx * (i + 1) - cnt) - 1);

        if(st > ed) continue;

        ret += 1LL * dp(idx - 1, cnt + i) * (ed - st + 1) % mod;
        ret %= mod;
        ret += 1LL * (mod - i) * (ed - st + 1) % mod * po[idx - 1] % mod;
        ret %= mod;
        ret += 1LL * (st + ed) * (ed - st + 1) / 2 % mod * po[idx - 1] % mod;
        ret %= mod;
    }
    //*
    if(idx + 1 <= K) {
        ret += 1LL * dp(idx - 1, cnt) * (K - idx) % mod;
        ret %= mod;
        ret += 1LL * (idx + 1 + K) * (K - idx) / 2 % mod * po[idx - 1] % mod;
        ret %= mod;
    }
    //*/
    return ret;
}

int main() {
    scanf("%d %d", &N, &K);

    po[0] = 1;
    for(int i = 1; i < 102; i++) {
        po[i] = 1LL * po[i - 1] * (K + 1) % mod;
    }

    memset(cc, -1, sizeof(cc));
    printf("%d", dp(N, 0));
}

```