#include <bits/stdc++.h>
using namespace std;
const int M = 1001, mod = 1e9 + 7;
int mul(int x, int y) { return 1LL * x * y % mod; }
void inc(int& x, int y) {
  x += y;
  if (x >= mod) x -= mod;
}
int n, dp[50][M], C[M][M], fac[M];
int cal(int k, int sum) {
  return mul(fac[k], mul(dp[k][sum], C[n - sum + k][k]));
}
int main() {
  dp[0][0] = 1;
  for (int i = 1; i <= 1000; i++) {
    for (int k = 1000; k >= i; k--) {
      for (int j = 45; j > 0; j--) {
        inc(dp[j][k], dp[j - 1][k - i]);
      }
    }
  }
  for (int i = 0; i <= 1000; i++) {
    for (int j = 0; j <= i; j++) {
      if (j == 0 || i == j)
        C[i][j] = 1;
      else
        inc(C[i][j], C[i - 1][j] + C[i - 1][j - 1]);
    }
  }
  fac[0] = 1;
  for (int i = 1; i <= 1000; i++) {
    fac[i] = mul(fac[i - 1], i);
  }
  int k, T;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &k);
    if (k > 45)
      puts("0");
    else {
      int ans = 0;
      for (int s = k; s <= n; s++) inc(ans, cal(k, s));
      printf("%d\n", ans);
    }
  }
}

### 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 M = 1001, mod = 1e9 + 7;
int mul(int x, int y) { return 1LL * x * y % mod; }
void inc(int& x, int y) {
  x += y;
  if (x >= mod) x -= mod;
}
int n, dp[50][M], C[M][M], fac[M];
int cal(int k, int sum) {
  return mul(fac[k], mul(dp[k][sum], C[n - sum + k][k]));
}
int main() {
  dp[0][0] = 1;
  for (int i = 1; i <= 1000; i++) {
    for (int k = 1000; k >= i; k--) {
      for (int j = 45; j > 0; j--) {
        inc(dp[j][k], dp[j - 1][k - i]);
      }
    }
  }
  for (int i = 0; i <= 1000; i++) {
    for (int j = 0; j <= i; j++) {
      if (j == 0 || i == j)
        C[i][j] = 1;
      else
        inc(C[i][j], C[i - 1][j] + C[i - 1][j - 1]);
    }
  }
  fac[0] = 1;
  for (int i = 1; i <= 1000; i++) {
    fac[i] = mul(fac[i - 1], i);
  }
  int k, T;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &k);
    if (k > 45)
      puts("0");
    else {
      int ans = 0;
      for (int s = k; s <= n; s++) inc(ans, cal(k, s));
      printf("%d\n", ans);
    }
  }
}

```