#include <bits/stdc++.h>
using namespace std;
const int MB = 2000, MAXN = 1000, MAXK = 50, MOD = 1000000007;
int fac[MAXN + 10], bi[MB + 10][MB + 10], dp[MAXK + 10][MAXN + 10];
inline void fadd(int &a, int b) {
  a += b;
  if (a >= MOD) {
    a -= MOD;
  }
}
void init() {
  bi[0][0] = 1;
  for (int i = 1; i <= MB; ++i) {
    bi[i][0] = bi[i][i] = 1;
    for (int j = 1; j < i; ++j) {
      bi[i][j] = (bi[i - 1][j] + bi[i - 1][j - 1]) % MOD;
    }
  }
  dp[0][0] = 1;
  for (int i = 1; i <= MAXN; ++i) {
    for (int k = MAXK; k > 0; --k) {
      for (int s = i; s <= MAXN; ++s) {
        fadd(dp[k][s], dp[k - 1][s - i]);
      }
    }
  }
  fac[0] = 1;
  for (int i = 1; i <= MAXN; ++i) {
    fac[i] = (long long)fac[i - 1] * i % MOD;
  }
}
int main(void) {
  init();
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d%d", &n, &k);
    long long res = 0;
    if (k < 50) {
      for (int s = 1; s <= n; ++s) {
        res += (long long)bi[n - s + k][k] * dp[k][s];
        if (s % 8 == 0) {
          res %= MOD;
        }
      }
      res %= MOD;
      res = (long long)res * fac[k] % MOD;
    }
    printf("%d\n", (int)res);
  }
  return 0;
}

### 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 MB = 2000, MAXN = 1000, MAXK = 50, MOD = 1000000007;
int fac[MAXN + 10], bi[MB + 10][MB + 10], dp[MAXK + 10][MAXN + 10];
inline void fadd(int &a, int b) {
  a += b;
  if (a >= MOD) {
    a -= MOD;
  }
}
void init() {
  bi[0][0] = 1;
  for (int i = 1; i <= MB; ++i) {
    bi[i][0] = bi[i][i] = 1;
    for (int j = 1; j < i; ++j) {
      bi[i][j] = (bi[i - 1][j] + bi[i - 1][j - 1]) % MOD;
    }
  }
  dp[0][0] = 1;
  for (int i = 1; i <= MAXN; ++i) {
    for (int k = MAXK; k > 0; --k) {
      for (int s = i; s <= MAXN; ++s) {
        fadd(dp[k][s], dp[k - 1][s - i]);
      }
    }
  }
  fac[0] = 1;
  for (int i = 1; i <= MAXN; ++i) {
    fac[i] = (long long)fac[i - 1] * i % MOD;
  }
}
int main(void) {
  init();
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d%d", &n, &k);
    long long res = 0;
    if (k < 50) {
      for (int s = 1; s <= n; ++s) {
        res += (long long)bi[n - s + k][k] * dp[k][s];
        if (s % 8 == 0) {
          res %= MOD;
        }
      }
      res %= MOD;
      res = (long long)res * fac[k] % MOD;
    }
    printf("%d\n", (int)res);
  }
  return 0;
}

```