#include <bits/stdc++.h>
using namespace std;
int c[1001][1001], f[1001], s[51][1001];
int main() {
  int i, j, k, T, m, n, t;
  c[0][0] = 1;
  for (i = 1; i <= 1000; i++) {
    c[i][0] = 1;
    for (j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % 1000000007;
  }
  f[0] = 1;
  for (i = 1; i <= 1000; i++) f[i] = (long long)i * f[i - 1] % 1000000007;
  s[0][0] = 1;
  for (int d = 0; d <= 1000; d++)
    for (k = min(49, d); k >= 0; k--)
      for (i = 0; i + d <= 1000; i++)
        s[k + 1][i + d] = (s[k + 1][i + d] + s[k][i]) % 1000000007;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &k);
    if (k > 50) {
      puts("0");
      continue;
    }
    long long ans = 0;
    for (i = k * (k - 1) / 2; i <= n; i++)
      ans += (long long)c[n - i][k] * s[k][i] % 1000000007, ans %= 1000000007;
    ans *= (long long)f[k];
    ans %= 1000000007;
    printf("%d\n", (int)ans);
  }
}

### 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;
int c[1001][1001], f[1001], s[51][1001];
int main() {
  int i, j, k, T, m, n, t;
  c[0][0] = 1;
  for (i = 1; i <= 1000; i++) {
    c[i][0] = 1;
    for (j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % 1000000007;
  }
  f[0] = 1;
  for (i = 1; i <= 1000; i++) f[i] = (long long)i * f[i - 1] % 1000000007;
  s[0][0] = 1;
  for (int d = 0; d <= 1000; d++)
    for (k = min(49, d); k >= 0; k--)
      for (i = 0; i + d <= 1000; i++)
        s[k + 1][i + d] = (s[k + 1][i + d] + s[k][i]) % 1000000007;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &k);
    if (k > 50) {
      puts("0");
      continue;
    }
    long long ans = 0;
    for (i = k * (k - 1) / 2; i <= n; i++)
      ans += (long long)c[n - i][k] * s[k][i] % 1000000007, ans %= 1000000007;
    ans *= (long long)f[k];
    ans %= 1000000007;
    printf("%d\n", (int)ans);
  }
}

```