#include <bits/stdc++.h>
using namespace std;
long long jc[1001 + 100], f[1001 + 100][1001 + 100], c[1001 + 100][1001 + 100],
    ans;
int n, k, T;
int main() {
  jc[0] = 1;
  for (int i = 1; i <= 1001; ++i) jc[i] = (jc[i - 1] * i) % 1000000007;
  f[0][0] = 1;
  for (int v = 1; v <= 1001; ++v) {
    for (int j = 1001; j >= v; --j) {
      for (int i = 1; i <= 45; ++i) {
        f[i][j] += f[i - 1][j - v], f[i][j] %= 1000000007;
      }
    }
  }
  for (int i = 0; i <= 1001; ++i) c[i][0] = 1;
  for (int i = 1; i <= 1001; ++i)
    for (int j = 1; j <= i; ++j)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % 1000000007;
  scanf("%d", &T);
  while (T--) {
    scanf("%d", &n), scanf("%d", &k);
    ans = 0;
    for (int i = k * (k + 1) / 2; i <= n; ++i)
      ans += (f[k][i] * c[n - i + k][k]) % 1000000007;
    ans %= 1000000007;
    ans = (ans * jc[k]) % 1000000007;
    printf("%I64d\n", ans);
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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;
long long jc[1001 + 100], f[1001 + 100][1001 + 100], c[1001 + 100][1001 + 100],
    ans;
int n, k, T;
int main() {
  jc[0] = 1;
  for (int i = 1; i <= 1001; ++i) jc[i] = (jc[i - 1] * i) % 1000000007;
  f[0][0] = 1;
  for (int v = 1; v <= 1001; ++v) {
    for (int j = 1001; j >= v; --j) {
      for (int i = 1; i <= 45; ++i) {
        f[i][j] += f[i - 1][j - v], f[i][j] %= 1000000007;
      }
    }
  }
  for (int i = 0; i <= 1001; ++i) c[i][0] = 1;
  for (int i = 1; i <= 1001; ++i)
    for (int j = 1; j <= i; ++j)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % 1000000007;
  scanf("%d", &T);
  while (T--) {
    scanf("%d", &n), scanf("%d", &k);
    ans = 0;
    for (int i = k * (k + 1) / 2; i <= n; ++i)
      ans += (f[k][i] * c[n - i + k][k]) % 1000000007;
    ans %= 1000000007;
    ans = (ans * jc[k]) % 1000000007;
    printf("%I64d\n", ans);
  }
  return 0;
}

```