#include <bits/stdc++.h>
using namespace std;
const int MX = 1010;
const long long MOD = 1000000007;
long long a[MX];
int f[MX][50][MX], g[2][50][MX];
void init() {
  a[0] = 1;
  for (int i = 1; i <= 1000; i++) {
    a[i] = (a[i - 1] * i) % MOD;
  }
  for (int i = 1; i <= 1000; i++) {
    for (int j = 1; j <= 45; j++) {
      for (int k = j; k <= 1000; k++) {
        if (j == 1) {
          if (k <= i) {
            g[i & 1][j][k] = (g[(i - 1) & 1][j][k] + 1) % MOD;
          } else {
            g[i & 1][j][k] = 0;
          }
        } else {
          if (k <= i) {
            g[i & 1][j][k] =
                (g[(i - 1) & 1][j][k] + f[i - k][j - 1][k - 1]) % MOD;
          } else {
            g[i & 1][j][k] = 0;
          }
        }
        f[i][j][k] = (f[i][j][k - 1] + g[i & 1][j][k]) % MOD;
      }
    }
  }
}
int main() {
  init();
  int t, n, k;
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d", &n, &k);
    if (k >= 50) {
      printf("0\n");
    } else {
      printf("%I64d\n", (long long)(f[n][k][1000]) * a[k] % MOD);
    }
  }
}

### Prompt

Create a solution in Cpp for 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;
const int MX = 1010;
const long long MOD = 1000000007;
long long a[MX];
int f[MX][50][MX], g[2][50][MX];
void init() {
  a[0] = 1;
  for (int i = 1; i <= 1000; i++) {
    a[i] = (a[i - 1] * i) % MOD;
  }
  for (int i = 1; i <= 1000; i++) {
    for (int j = 1; j <= 45; j++) {
      for (int k = j; k <= 1000; k++) {
        if (j == 1) {
          if (k <= i) {
            g[i & 1][j][k] = (g[(i - 1) & 1][j][k] + 1) % MOD;
          } else {
            g[i & 1][j][k] = 0;
          }
        } else {
          if (k <= i) {
            g[i & 1][j][k] =
                (g[(i - 1) & 1][j][k] + f[i - k][j - 1][k - 1]) % MOD;
          } else {
            g[i & 1][j][k] = 0;
          }
        }
        f[i][j][k] = (f[i][j][k - 1] + g[i & 1][j][k]) % MOD;
      }
    }
  }
}
int main() {
  init();
  int t, n, k;
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d", &n, &k);
    if (k >= 50) {
      printf("0\n");
    } else {
      printf("%I64d\n", (long long)(f[n][k][1000]) * a[k] % MOD);
    }
  }
}

```