#include <bits/stdc++.h>
using namespace std;
stringstream ss;
long long mod = 1000000007LL;
int dp[51][1024][1024];
int C[2048][2048], F[51];
void pre() {
  for (int i = F[0] = 1; i < 51; i++) F[i] = (long long)F[i - 1] * i % mod;
  for (int i = 0; i < 2048; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++)
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
  }
  dp[0][0][1] = 1;
  for (int i = 0; i < 50; i++)
    for (int j = 0; j < 1010; j++)
      for (int k = 0; k < 1010; k++) {
        dp[i][j][k + 1] = (dp[i][j][k + 1] + dp[i][j][k]) % mod;
        if (j + k < 1024)
          dp[i + 1][j + k][k + 1] =
              (dp[i + 1][j + k][k + 1] + dp[i][j][k]) % mod;
      }
}
int main() {
  pre();
  int n, k, t;
  long long ans = 0;
  cin >> t;
  while (t--) {
    cin >> n >> k;
    if (k >= 50)
      cout << 0 << endl;
    else {
      for (int i = ans = 0; i <= n; i++)
        ans = (ans +
               (((long long)dp[k][i][n + 1] * F[k] % mod) * C[n - i + k][k]) %
                   mod) %
              mod;
      cout << ans << endl;
    }
  }
  return 0;
}

### Prompt

Please create a solution in Cpp 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>
using namespace std;
stringstream ss;
long long mod = 1000000007LL;
int dp[51][1024][1024];
int C[2048][2048], F[51];
void pre() {
  for (int i = F[0] = 1; i < 51; i++) F[i] = (long long)F[i - 1] * i % mod;
  for (int i = 0; i < 2048; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++)
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
  }
  dp[0][0][1] = 1;
  for (int i = 0; i < 50; i++)
    for (int j = 0; j < 1010; j++)
      for (int k = 0; k < 1010; k++) {
        dp[i][j][k + 1] = (dp[i][j][k + 1] + dp[i][j][k]) % mod;
        if (j + k < 1024)
          dp[i + 1][j + k][k + 1] =
              (dp[i + 1][j + k][k + 1] + dp[i][j][k]) % mod;
      }
}
int main() {
  pre();
  int n, k, t;
  long long ans = 0;
  cin >> t;
  while (t--) {
    cin >> n >> k;
    if (k >= 50)
      cout << 0 << endl;
    else {
      for (int i = ans = 0; i <= n; i++)
        ans = (ans +
               (((long long)dp[k][i][n + 1] * F[k] % mod) * C[n - i + k][k]) %
                   mod) %
              mod;
      cout << ans << endl;
    }
  }
  return 0;
}

```