#include <bits/stdc++.h>
using namespace std;
const long long MD = 1e9 + 7.1;
const int MN = 1010;
int dp[MN][50];
long long f[MN];
int solve(int n, int k) {
  if (n < 0) return 0;
  if (!k) return 1;
  if (n == 0) return 0;
  if (dp[n][k] != -1) return dp[n][k];
  long long r = solve(n - 1, k);
  for (int i = 0; i < n; i++) {
    r += solve(n - i - 1 - (k - 1) * (i + 1), k - 1);
  }
  r %= MD;
  dp[n][k] = (int)r;
  return (int)r;
}
int main() {
  f[0] = 1;
  for (int i = 1; i < MN; i++) {
    f[i] = f[i - 1] * i % MD;
  }
  fill_n(dp[0], MN * 50, -1);
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    scanf("%d %d", &n, &k);
    if (k < 50) {
      printf("%d\n", (int)(f[k] * solve(n, k) % MD));
    } else {
      printf("0\n");
    }
  }
  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 long long MD = 1e9 + 7.1;
const int MN = 1010;
int dp[MN][50];
long long f[MN];
int solve(int n, int k) {
  if (n < 0) return 0;
  if (!k) return 1;
  if (n == 0) return 0;
  if (dp[n][k] != -1) return dp[n][k];
  long long r = solve(n - 1, k);
  for (int i = 0; i < n; i++) {
    r += solve(n - i - 1 - (k - 1) * (i + 1), k - 1);
  }
  r %= MD;
  dp[n][k] = (int)r;
  return (int)r;
}
int main() {
  f[0] = 1;
  for (int i = 1; i < MN; i++) {
    f[i] = f[i - 1] * i % MD;
  }
  fill_n(dp[0], MN * 50, -1);
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    scanf("%d %d", &n, &k);
    if (k < 50) {
      printf("%d\n", (int)(f[k] * solve(n, k) % MD));
    } else {
      printf("0\n");
    }
  }
  return 0;
}

```