#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
#include <map>
#include <string>

using namespace std;

#define fastInp cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(0);

typedef long long ll;
const ll MOD = 1e9 + 7, SZ = 5002;

ll n, k, dp[SZ][SZ * 2];

int main() {
	fastInp;

	cin >> n >> k;

	dp[0][0] = 1;
	ll pw = 1;
	for (int i = 0; i < n - 1; i++) {
		pw *= (k + 1);
		pw %= MOD;
	}
	ll add = 0;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j <= k; j++) {
			add += (j * pw);
			add %= MOD;
			for (int curs = 0; curs < SZ * 2; curs++) {
				ll s = 0;
				if (j > (n - i)) {
					s = curs;
				}
				else {
					s = curs + (curs + j) / (n - i);
				}
				dp[i + 1][s] += dp[i][curs];
				dp[i + 1][s] %= MOD;
			}
		}
	}

	ll dis = 0;
	for (int j = 0; j < SZ * 2; j++) {
		dis += dp[n][j] * j;
		dis %= MOD;
	}
	cout << (add - dis + MOD) % MOD;

	return 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 <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
#include <map>
#include <string>

using namespace std;

#define fastInp cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(0);

typedef long long ll;
const ll MOD = 1e9 + 7, SZ = 5002;

ll n, k, dp[SZ][SZ * 2];

int main() {
	fastInp;

	cin >> n >> k;

	dp[0][0] = 1;
	ll pw = 1;
	for (int i = 0; i < n - 1; i++) {
		pw *= (k + 1);
		pw %= MOD;
	}
	ll add = 0;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j <= k; j++) {
			add += (j * pw);
			add %= MOD;
			for (int curs = 0; curs < SZ * 2; curs++) {
				ll s = 0;
				if (j > (n - i)) {
					s = curs;
				}
				else {
					s = curs + (curs + j) / (n - i);
				}
				dp[i + 1][s] += dp[i][curs];
				dp[i + 1][s] %= MOD;
			}
		}
	}

	ll dis = 0;
	for (int j = 0; j < SZ * 2; j++) {
		dis += dp[n][j] * j;
		dis %= MOD;
	}
	cout << (add - dis + MOD) % MOD;

	return 0;
}
```