#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> PII;

#define fi first
#define se second
#define mp make_pair
#define pb push_back

#define P 1000000007
#define N 110
#define MM 4010
int f[N][MM];
int n, kk;

int main() {
	/*
	int sg = 0;
	for (int i = 100; i >= 1; i--) {
		sg += (sg + i)/i;
	}
	cout << sg << endl;
	*/
	cin >> n >> kk;
	f[n][0] = 1;
	for (int i = n-1; i >= 0; i--)
		for (int j = 0; j < MM; j ++) if (f[i+1][j]) {
			for (int k = 0; k <= kk; k ++) {
				int sg = j;
				if (k <= i+1) sg = j + (j + k)/(i+1);
				(f[i][sg] += f[i+1][j]) %= P;
			}
		}
	//for (int i = 0; i < MM; i ++)
	//	if (f[0][i]) printf ("%d %d\n", i, f[0][i]);
	int S = 0;
	for (int i = 0; i < MM; i ++)
		S = (S + (ll)f[0][i]*i%P)%P;
	int T = (ll)kk*(P+1)/2%P;
	T = (ll)T*n%P;
	for (int i = 0; i < n; i ++)
		T = (ll)T*(kk+1)%P;
	printf ("%d\n", (T-S+P)%P);
	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 <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> PII;

#define fi first
#define se second
#define mp make_pair
#define pb push_back

#define P 1000000007
#define N 110
#define MM 4010
int f[N][MM];
int n, kk;

int main() {
	/*
	int sg = 0;
	for (int i = 100; i >= 1; i--) {
		sg += (sg + i)/i;
	}
	cout << sg << endl;
	*/
	cin >> n >> kk;
	f[n][0] = 1;
	for (int i = n-1; i >= 0; i--)
		for (int j = 0; j < MM; j ++) if (f[i+1][j]) {
			for (int k = 0; k <= kk; k ++) {
				int sg = j;
				if (k <= i+1) sg = j + (j + k)/(i+1);
				(f[i][sg] += f[i+1][j]) %= P;
			}
		}
	//for (int i = 0; i < MM; i ++)
	//	if (f[0][i]) printf ("%d %d\n", i, f[0][i]);
	int S = 0;
	for (int i = 0; i < MM; i ++)
		S = (S + (ll)f[0][i]*i%P)%P;
	int T = (ll)kk*(P+1)/2%P;
	T = (ll)T*n%P;
	for (int i = 0; i < n; i ++)
		T = (ll)T*(kk+1)%P;
	printf ("%d\n", (T-S+P)%P);
	return 0;
}
```