#include <bits/stdc++.h>
using namespace std;
int d[1010][1010], C[1010][1010], A[1010][1010];
const int M = 1e9 + 7;
int main() {
  int i, j, t;
  C[0][0] = 1;
  for (i = 1; i <= 1005; i++) C[0][i] = ((long long)C[0][i - 1] * i) % M;
  for (i = 1; i <= 1005; i++) {
    C[i][0] = 1;
    for (j = 1; j <= 1005; j++) {
      C[i][j] = ((long long)C[i][j - 1] * (i + j)) % M;
    }
  }
  d[0][0] = 1;
  d[1][0] = 0;
  d[1][1] = 1;
  for (i = 2; i <= 1005; i++) {
    d[i][0] = 0;
    for (j = 1; j <= min(i, 50); j++)
      d[i][j] = (d[i - j][j - 1] + d[i - j][j]) % M;
  }
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d%d", &n, &k);
    long long ans = 0;
    for (i = 1; i <= n; i++) ans += ((long long)d[i][k] * C[n - i][k]) % M;
    printf("%lld\n", ans % M);
  }
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 d[1010][1010], C[1010][1010], A[1010][1010];
const int M = 1e9 + 7;
int main() {
  int i, j, t;
  C[0][0] = 1;
  for (i = 1; i <= 1005; i++) C[0][i] = ((long long)C[0][i - 1] * i) % M;
  for (i = 1; i <= 1005; i++) {
    C[i][0] = 1;
    for (j = 1; j <= 1005; j++) {
      C[i][j] = ((long long)C[i][j - 1] * (i + j)) % M;
    }
  }
  d[0][0] = 1;
  d[1][0] = 0;
  d[1][1] = 1;
  for (i = 2; i <= 1005; i++) {
    d[i][0] = 0;
    for (j = 1; j <= min(i, 50); j++)
      d[i][j] = (d[i - j][j - 1] + d[i - j][j]) % M;
  }
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d%d", &n, &k);
    long long ans = 0;
    for (i = 1; i <= n; i++) ans += ((long long)d[i][k] * C[n - i][k]) % M;
    printf("%lld\n", ans % M);
  }
  return 0;
}

```