#include <bits/stdc++.h>
using namespace std;
const int Mod = 1e9 + 7;
int g[53][1003][1003], f[53][1003];
int C[1053][53];
int n, k, Q;
int main() {
  g[0][0][1] = 1;
  for (int i = 0, Fac = 1; i < 51; i++, Fac = (1LL * Fac * i) % Mod)
    for (int j = 0; j <= 1001; j++) {
      int _s = 0;
      for (int k = 1; j + k <= 1001; k++) {
        (_s += g[i][j][k]) %= Mod;
        (g[i + 1][j + k][k + 1] += _s) %= Mod;
      }
      for (int k = 1; k <= 1001; k++) (f[i][j] += g[i][j][k]) %= Mod;
      f[i][j] = 1LL * f[i][j] * Fac % Mod;
    }
  for (int i = 0; i <= 1051; i++) {
    C[i][0] = 1;
    for (int j = 1, _ = min(51, i); j <= _; j++)
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % Mod;
  }
  scanf("%d", &Q);
  while (Q--) {
    scanf("%d%d", &n, &k);
    if (k > 51) {
      puts("0");
      continue;
    }
    int Ans = 0;
    for (int sum = 0; sum <= n; sum++)
      (Ans += 1LL * f[k][sum] * C[n - sum + k][k] % Mod) %= Mod;
    printf("%d\n", Ans);
  }
}

### Prompt

Please provide a CPP coded solution 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 Mod = 1e9 + 7;
int g[53][1003][1003], f[53][1003];
int C[1053][53];
int n, k, Q;
int main() {
  g[0][0][1] = 1;
  for (int i = 0, Fac = 1; i < 51; i++, Fac = (1LL * Fac * i) % Mod)
    for (int j = 0; j <= 1001; j++) {
      int _s = 0;
      for (int k = 1; j + k <= 1001; k++) {
        (_s += g[i][j][k]) %= Mod;
        (g[i + 1][j + k][k + 1] += _s) %= Mod;
      }
      for (int k = 1; k <= 1001; k++) (f[i][j] += g[i][j][k]) %= Mod;
      f[i][j] = 1LL * f[i][j] * Fac % Mod;
    }
  for (int i = 0; i <= 1051; i++) {
    C[i][0] = 1;
    for (int j = 1, _ = min(51, i); j <= _; j++)
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % Mod;
  }
  scanf("%d", &Q);
  while (Q--) {
    scanf("%d%d", &n, &k);
    if (k > 51) {
      puts("0");
      continue;
    }
    int Ans = 0;
    for (int sum = 0; sum <= n; sum++)
      (Ans += 1LL * f[k][sum] * C[n - sum + k][k] % Mod) %= Mod;
    printf("%d\n", Ans);
  }
}

```