#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000007;
long long f, c[2100][2100], dp[1100][1100], k, t, n, m, x[1100][1100], ans1;
int main() {
  f = 1;
  for (int i = 0; i <= 2000; i++) {
    c[i][0] = 1;
    c[i][i] = 1;
  }
  for (int i = 0; i <= 1000; i++) {
    x[i][1] = 1;
    for (int j = 2; j <= 1000; j++) {
      x[i][j] = x[i][j - 1];
      if (j <= i) {
        x[i][j] += x[i - j][j];
        x[i][j] = x[i][j] % MOD;
      }
    }
  }
  for (int i = 2; i <= 2000; i++)
    for (int j = 1; j < i; j++) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % MOD;
  for (int i = 1; i <= 1000; i++) {
    f *= i;
    f = f % MOD;
    k = i * (i + 1) / 2;
    if (k > 1000) break;
    dp[i][k] = f;
    for (int j = k + 1; j <= 1000; j++) {
      m = j - k;
      for (int u = 0; u <= m; u++) {
        ans1 = (c[u + i][i] * x[m - u][i]) % MOD;
        dp[i][j] += (ans1 * f) % MOD;
        if (dp[i][j] < 0) {
          cout << i << " " << j << " " << dp[i][j] << endl;
        }
        dp[i][j] = dp[i][j] % MOD;
      }
    }
  }
  cin >> t;
  for (int i = 0; i < t; i++) {
    cin >> n >> k;
    cout << dp[k][n] << endl;
  }
}

### 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;
const long long MOD = 1000000007;
long long f, c[2100][2100], dp[1100][1100], k, t, n, m, x[1100][1100], ans1;
int main() {
  f = 1;
  for (int i = 0; i <= 2000; i++) {
    c[i][0] = 1;
    c[i][i] = 1;
  }
  for (int i = 0; i <= 1000; i++) {
    x[i][1] = 1;
    for (int j = 2; j <= 1000; j++) {
      x[i][j] = x[i][j - 1];
      if (j <= i) {
        x[i][j] += x[i - j][j];
        x[i][j] = x[i][j] % MOD;
      }
    }
  }
  for (int i = 2; i <= 2000; i++)
    for (int j = 1; j < i; j++) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % MOD;
  for (int i = 1; i <= 1000; i++) {
    f *= i;
    f = f % MOD;
    k = i * (i + 1) / 2;
    if (k > 1000) break;
    dp[i][k] = f;
    for (int j = k + 1; j <= 1000; j++) {
      m = j - k;
      for (int u = 0; u <= m; u++) {
        ans1 = (c[u + i][i] * x[m - u][i]) % MOD;
        dp[i][j] += (ans1 * f) % MOD;
        if (dp[i][j] < 0) {
          cout << i << " " << j << " " << dp[i][j] << endl;
        }
        dp[i][j] = dp[i][j] % MOD;
      }
    }
  }
  cin >> t;
  for (int i = 0; i < t; i++) {
    cin >> n >> k;
    cout << dp[k][n] << endl;
  }
}

```