#include <bits/stdc++.h>
using namespace std;
const int N = 1024;
const int K = 50;
const long long mod = 1000000007;
long long binom[N][N] = {1}, fact[N] = {1}, d[K][N] = {1};
void prepare() {
  for (int i = 1; i < N; ++i) {
    binom[i][0] = 1;
    for (int j = 1; j <= i; ++j) {
      binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
      if (binom[i][j] >= mod) binom[i][j] -= mod;
    }
  }
  for (int i = 1; i < (N); ++i) fact[i] = fact[i - 1] * i % mod;
  for (int i = 0; i < (N); ++i)
    for (int j = K - 1; j >= 1; --j)
      for (int k = i; k < (N); ++k) {
        d[j][k] += d[j - 1][k - i];
        if (d[j][k] >= mod) d[j][k] -= mod;
      }
}
void solve(int n, int k) {
  long long ans = 0;
  for (int m = k * (k - 1) / 2; m <= n - k; ++m) {
    ans += binom[n - m][k] * d[k][m] % mod * fact[k] % mod;
  }
  cout << ans % mod << endl;
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  prepare();
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    solve(n, k);
  }
  return 0;
}

### Prompt

Your task is to create 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 = 1024;
const int K = 50;
const long long mod = 1000000007;
long long binom[N][N] = {1}, fact[N] = {1}, d[K][N] = {1};
void prepare() {
  for (int i = 1; i < N; ++i) {
    binom[i][0] = 1;
    for (int j = 1; j <= i; ++j) {
      binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
      if (binom[i][j] >= mod) binom[i][j] -= mod;
    }
  }
  for (int i = 1; i < (N); ++i) fact[i] = fact[i - 1] * i % mod;
  for (int i = 0; i < (N); ++i)
    for (int j = K - 1; j >= 1; --j)
      for (int k = i; k < (N); ++k) {
        d[j][k] += d[j - 1][k - i];
        if (d[j][k] >= mod) d[j][k] -= mod;
      }
}
void solve(int n, int k) {
  long long ans = 0;
  for (int m = k * (k - 1) / 2; m <= n - k; ++m) {
    ans += binom[n - m][k] * d[k][m] % mod * fact[k] % mod;
  }
  cout << ans % mod << endl;
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  prepare();
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    solve(n, k);
  }
  return 0;
}

```