#include <bits/stdc++.h>
const int p = 1000000007;
int c[1105][1105], d[1005], f[1005][50][1005];
int h, i, j, k, m, n, s, t;
int main() {
  d[0] = 1;
  for (i = 1; i <= 1001; i++) d[i] = 1LL * i * d[i - 1] % p;
  for (i = 0; i <= 1100; i++)
    for (j = 0; j <= i; j++)
      if ((j == 0) && (j == i))
        c[i][j] = 1;
      else
        c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % p;
  f[0][0][1] = 1;
  for (j = 0; j < 50; j++)
    for (i = 0; i <= 1000; i++)
      for (k = 1; k <= 1001; k++) {
        f[i][j][k] = (f[i][j][k] + f[i][j][k - 1]) % p;
        if (i + k <= 1000)
          f[i + k][j + 1][k + 1] = (f[i + k][j + 1][k + 1] + f[i][j][k]) % p;
      }
  scanf("%d", &t);
  for (h = 1; h <= t; h++) {
    scanf("%d%d", &n, &m);
    if (m >= 50)
      printf("0\n");
    else {
      s = 0;
      for (i = 0; i <= n; i++)
        s = (s + 1LL * f[i][m][1001] * d[m] % p * c[n - i + m][m] % p) % p;
      printf("%d\n", s);
    }
  }
  return 0;
}

### Prompt

Your task is to create 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>
const int p = 1000000007;
int c[1105][1105], d[1005], f[1005][50][1005];
int h, i, j, k, m, n, s, t;
int main() {
  d[0] = 1;
  for (i = 1; i <= 1001; i++) d[i] = 1LL * i * d[i - 1] % p;
  for (i = 0; i <= 1100; i++)
    for (j = 0; j <= i; j++)
      if ((j == 0) && (j == i))
        c[i][j] = 1;
      else
        c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % p;
  f[0][0][1] = 1;
  for (j = 0; j < 50; j++)
    for (i = 0; i <= 1000; i++)
      for (k = 1; k <= 1001; k++) {
        f[i][j][k] = (f[i][j][k] + f[i][j][k - 1]) % p;
        if (i + k <= 1000)
          f[i + k][j + 1][k + 1] = (f[i + k][j + 1][k + 1] + f[i][j][k]) % p;
      }
  scanf("%d", &t);
  for (h = 1; h <= t; h++) {
    scanf("%d%d", &n, &m);
    if (m >= 50)
      printf("0\n");
    else {
      s = 0;
      for (i = 0; i <= n; i++)
        s = (s + 1LL * f[i][m][1001] * d[m] % p * c[n - i + m][m] % p) % p;
      printf("%d\n", s);
    }
  }
  return 0;
}

```