#include <bits/stdc++.h>
using namespace std;
int C[1005][1005], fac[1005], dp[1005][51];
void init() {
  C[0][0] = 1;
  for (int i = 1; i <= 1000; ++i) {
    C[i][0] = 1;
    for (int j = 1; j <= i; ++j)
      C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % 1000000007;
  }
  fac[0] = 1;
  for (int i = 1; i <= 1000; ++i) fac[i] = (fac[i - 1] + 0LL) * i % 1000000007;
  dp[0][0] = 1;
  for (int n = 1; n <= 1000; ++n)
    for (int k = 1; k <= 50; ++k)
      for (int i = 1; i * k <= n; ++i)
        dp[n][k] = (dp[n][k] + dp[n - i * k][k - 1]) % 1000000007;
}
int main() {
  init();
  int t, n, k;
  cin >> t;
  while (t--) {
    scanf("%d%d", &n, &k);
    int ans = 0;
    for (int sum = k * (k + 1) / 2; sum <= n; ++sum) {
      ans += (dp[sum][k] + 0LL) * C[n - sum + k][k] % 1000000007;
      ans %= 1000000007;
    }
    ans = (ans + 0LL) * fac[k] % 1000000007;
    printf("%d\n", ans);
  }
  return 0;
}

### 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[1005][1005], fac[1005], dp[1005][51];
void init() {
  C[0][0] = 1;
  for (int i = 1; i <= 1000; ++i) {
    C[i][0] = 1;
    for (int j = 1; j <= i; ++j)
      C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % 1000000007;
  }
  fac[0] = 1;
  for (int i = 1; i <= 1000; ++i) fac[i] = (fac[i - 1] + 0LL) * i % 1000000007;
  dp[0][0] = 1;
  for (int n = 1; n <= 1000; ++n)
    for (int k = 1; k <= 50; ++k)
      for (int i = 1; i * k <= n; ++i)
        dp[n][k] = (dp[n][k] + dp[n - i * k][k - 1]) % 1000000007;
}
int main() {
  init();
  int t, n, k;
  cin >> t;
  while (t--) {
    scanf("%d%d", &n, &k);
    int ans = 0;
    for (int sum = k * (k + 1) / 2; sum <= n; ++sum) {
      ans += (dp[sum][k] + 0LL) * C[n - sum + k][k] % 1000000007;
      ans %= 1000000007;
    }
    ans = (ans + 0LL) * fac[k] % 1000000007;
    printf("%d\n", ans);
  }
  return 0;
}

```