#include <bits/stdc++.h>
using namespace std;
const int N = 1005, K = 50, MOD = 1e9 + 7;
long long ans[N][K], dp[N][K], fact[N], comb[N + K][K];
int main() {
  comb[0][0] = 1;
  for (int i = 1; i < N + K; ++i) {
    for (int j = 0; j < K; ++j) {
      comb[i][j] = comb[i - 1][j];
      if (j) comb[i][j] = (comb[i][j] + comb[i - 1][j - 1]) % MOD;
    }
  }
  fact[0] = 1;
  for (int i = 1; i < N; ++i) fact[i] = (fact[i - 1] * i) % MOD;
  dp[0][0] = 1;
  for (int i = 1; i < N; ++i) {
    for (int j = N - i - 1; j >= 0; --j) {
      for (int k = K - 2; k >= 0; --k) {
        dp[j + i][k + 1] += dp[j][k];
        dp[j + i][k + 1] %= MOD;
      }
    }
  }
  for (int i = 0; i < N; ++i)
    for (int k = 0; k < K; ++k) {
      dp[i][k] = (dp[i][k] * fact[k]) % MOD;
      for (int j = i; j < N; ++j) {
        ans[j][k] = (ans[j][k] + dp[i][k] * comb[j - i + k][k]) % MOD;
      }
    }
  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int n, k;
    scanf("%d %d", &n, &k);
    if (k >= K)
      puts("0");
    else
      printf("%d\n", (int)ans[n][k]);
  }
}

### Prompt

Your challenge is to write a CPP solution 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;
const int N = 1005, K = 50, MOD = 1e9 + 7;
long long ans[N][K], dp[N][K], fact[N], comb[N + K][K];
int main() {
  comb[0][0] = 1;
  for (int i = 1; i < N + K; ++i) {
    for (int j = 0; j < K; ++j) {
      comb[i][j] = comb[i - 1][j];
      if (j) comb[i][j] = (comb[i][j] + comb[i - 1][j - 1]) % MOD;
    }
  }
  fact[0] = 1;
  for (int i = 1; i < N; ++i) fact[i] = (fact[i - 1] * i) % MOD;
  dp[0][0] = 1;
  for (int i = 1; i < N; ++i) {
    for (int j = N - i - 1; j >= 0; --j) {
      for (int k = K - 2; k >= 0; --k) {
        dp[j + i][k + 1] += dp[j][k];
        dp[j + i][k + 1] %= MOD;
      }
    }
  }
  for (int i = 0; i < N; ++i)
    for (int k = 0; k < K; ++k) {
      dp[i][k] = (dp[i][k] * fact[k]) % MOD;
      for (int j = i; j < N; ++j) {
        ans[j][k] = (ans[j][k] + dp[i][k] * comb[j - i + k][k]) % MOD;
      }
    }
  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int n, k;
    scanf("%d %d", &n, &k);
    if (k >= K)
      puts("0");
    else
      printf("%d\n", (int)ans[n][k]);
  }
}

```