#include <bits/stdc++.h>
using namespace std;
const int N = 1003;
const int mod = 1e9 + 7;
long long dp[N][N], C[N][N], A[N];
long long ans[N][N];
int n, k;
void add(long long &a, long long b) {
  a += b;
  if (a >= mod) a -= mod;
}
int main() {
  int i, j;
  A[0] = 1;
  for (i = 1; i < N; i++) A[i] = A[i - 1] * i % mod;
  for (i = 0; i < N; i++) {
    C[i][0] = C[i][i] = 1;
    for (j = 1; j < i; j++) C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
  }
  dp[0][0] = 1;
  for (i = 1; i < N; i++)
    for (j = i; j < N; j++) dp[i][j] = (dp[i - 1][j - i] + dp[i][j - i]) % mod;
  for (i = 1; i < N; i++)
    for (j = 1; j <= i && j <= 50; j++) {
      long long &val = ans[i][j];
      for (k = 1; k <= i; k++) {
        int t = i - k;
        add(val, dp[j][k] * C[j + t][t] % mod);
      }
      val = val * A[j] % mod;
    }
  int m;
  scanf("%d", &m);
  while (m--) {
    scanf("%d%d", &n, &k);
    printf("%I64d\n", ans[n][k]);
  }
  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 N = 1003;
const int mod = 1e9 + 7;
long long dp[N][N], C[N][N], A[N];
long long ans[N][N];
int n, k;
void add(long long &a, long long b) {
  a += b;
  if (a >= mod) a -= mod;
}
int main() {
  int i, j;
  A[0] = 1;
  for (i = 1; i < N; i++) A[i] = A[i - 1] * i % mod;
  for (i = 0; i < N; i++) {
    C[i][0] = C[i][i] = 1;
    for (j = 1; j < i; j++) C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
  }
  dp[0][0] = 1;
  for (i = 1; i < N; i++)
    for (j = i; j < N; j++) dp[i][j] = (dp[i - 1][j - i] + dp[i][j - i]) % mod;
  for (i = 1; i < N; i++)
    for (j = 1; j <= i && j <= 50; j++) {
      long long &val = ans[i][j];
      for (k = 1; k <= i; k++) {
        int t = i - k;
        add(val, dp[j][k] * C[j + t][t] % mod);
      }
      val = val * A[j] % mod;
    }
  int m;
  scanf("%d", &m);
  while (m--) {
    scanf("%d%d", &n, &k);
    printf("%I64d\n", ans[n][k]);
  }
  return 0;
}

```