#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1005;
const int MOD = 1000000007;
long long dp[2][MAXN][55], fact[MAXN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  fact[0] = 1;
  for (int i = 1; i < MAXN; i++) fact[i] = fact[i - 1] * i % MOD;
  int f = 0;
  for (int k = 0; k < MAXN; k++) {
    dp[f][0][0] = 1;
    for (int j = 1; j < MAXN; j++) {
      for (int i = 0; i < 55; i++) {
        dp[f][j][i] =
            dp[f][j - 1][i] + dp[1 - f][j][i] - dp[1 - f][j - 1][i] + MOD;
        if (j - k >= 0 && i - 1 >= 0) dp[f][j][i] += dp[1 - f][j - k][i - 1];
        dp[f][j][i] %= MOD;
      }
    }
    f = 1 - f;
  }
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    long long ans = 0;
    if (k * (k + 1) / 2 <= n) ans = dp[f][n][k] * fact[k] % MOD;
    cout << ans << '\n';
  }
  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;
const int MAXN = 1005;
const int MOD = 1000000007;
long long dp[2][MAXN][55], fact[MAXN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  fact[0] = 1;
  for (int i = 1; i < MAXN; i++) fact[i] = fact[i - 1] * i % MOD;
  int f = 0;
  for (int k = 0; k < MAXN; k++) {
    dp[f][0][0] = 1;
    for (int j = 1; j < MAXN; j++) {
      for (int i = 0; i < 55; i++) {
        dp[f][j][i] =
            dp[f][j - 1][i] + dp[1 - f][j][i] - dp[1 - f][j - 1][i] + MOD;
        if (j - k >= 0 && i - 1 >= 0) dp[f][j][i] += dp[1 - f][j - k][i - 1];
        dp[f][j][i] %= MOD;
      }
    }
    f = 1 - f;
  }
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    long long ans = 0;
    if (k * (k + 1) / 2 <= n) ans = dp[f][n][k] * fact[k] % MOD;
    cout << ans << '\n';
  }
  return 0;
}

```