#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
int const N = 1000 + 2, K = 45 + 2, mod = 1e9 + 7;
int T;
int dp[N][K], res[N][K];
int C[N][N];
void calc() {
  for (int i = 0; i < N; i++) {
    C[i][0] = C[i][i] = 1;
    for (int j = 1; j < i; j++) C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
  }
  dp[0][0] = 1;
  for (int d = 0; d < N; d++)
    for (int k = K - 2; k >= 0; k--)
      for (int i = 0; i + d < N; i++)
        dp[i + d][k + 1] = (dp[i + d][k + 1] + 1ll * (k + 1) * dp[i][k]) % mod;
  for (int i = 0; i < N; i++)
    for (int k = 0; k < K; k++)
      for (int j = 0; j <= i; j++)
        res[i][k] = (res[i][k] + 1ll * dp[j][k] * C[i - j][k]) % mod;
}
int main() {
  calc();
  scanf("%d ", &T);
  while (T--) {
    int n, k;
    scanf("%d %d ", &n, &k);
    printf("%d\n", (k < K ? res[n][k] : 0));
  }
}

### Prompt

Please formulate a CPP solution to the following problem:

The sequence of integer pairs (a1, b1), (a2, b2), ..., (ak, bk) is beautiful, if the following statements are fulfilled: 

  * 1 ≤ a1 ≤ b1 < a2 ≤ b2 < ... < ak ≤ bk ≤ n, where n is a given positive integer; 
  * all numbers b1 - a1, b2 - a2, ..., bk - ak are distinct. 



For the given number n find the number of beautiful sequences of length k. As the answer can be rather large, print the remainder after dividing it by 1000000007 (109 + 7).

Input

The first line contains integer t (1 ≤ t ≤ 2·105) — the number of the test data.

Each of the next t lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000).

Output

For each test from the input print the answer to the problem modulo 1000000007 (109 + 7). Print the answers to the tests in the order in which the tests are given in the input.

Examples

Input

6
1 1
2 1
2 2
3 1
3 2
3 3


Output

1
3
0
6
2
0

Note

In the first test sample there is exactly one beautiful sequence: (1, 1).

In the second test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (2, 2). 



In the fourth test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (1, 3); 
  * (2, 2); 
  * (2, 3); 
  * (3, 3). 



In the fifth test sample, the following sequences are beautiful: 

  * (1, 1), (2, 3); 
  * (1, 2), (3, 3). 



In the third and sixth samples, there are no beautiful sequences.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
int const N = 1000 + 2, K = 45 + 2, mod = 1e9 + 7;
int T;
int dp[N][K], res[N][K];
int C[N][N];
void calc() {
  for (int i = 0; i < N; i++) {
    C[i][0] = C[i][i] = 1;
    for (int j = 1; j < i; j++) C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
  }
  dp[0][0] = 1;
  for (int d = 0; d < N; d++)
    for (int k = K - 2; k >= 0; k--)
      for (int i = 0; i + d < N; i++)
        dp[i + d][k + 1] = (dp[i + d][k + 1] + 1ll * (k + 1) * dp[i][k]) % mod;
  for (int i = 0; i < N; i++)
    for (int k = 0; k < K; k++)
      for (int j = 0; j <= i; j++)
        res[i][k] = (res[i][k] + 1ll * dp[j][k] * C[i - j][k]) % mod;
}
int main() {
  calc();
  scanf("%d ", &T);
  while (T--) {
    int n, k;
    scanf("%d %d ", &n, &k);
    printf("%d\n", (k < K ? res[n][k] : 0));
  }
}

```