#include <bits/stdc++.h>
using namespace std;
constexpr int N = 1000 + 10;
constexpr int M = 70;
constexpr int MOD = 1e9 + 7;
long long t, n, m, fact[N], B[N][N], ch[N][N], dp[N][N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  fact[0] = 1;
  for (int i = 1; i < N; i++) fact[i] = (fact[i - 1] * i) % MOD;
  for (int i = 0; i < N; i++) {
    for (int j = 0; j <= i; j++) {
      if (!j || i == j) {
        ch[i][j] = 1;
        continue;
      }
      ch[i][j] = (ch[i - 1][j] + ch[i - 1][j - 1]) % MOD;
    }
  }
  B[0][0] = B[0][1] = 1;
  for (int i = 1; i < N; i++)
    for (int j = N - 1; j >= i; j--)
      for (int k = 1; k < M; k++) B[j][k] = (B[j][k] + B[j - i][k - 1]) % MOD;
  for (int i = 1; i < N; i++)
    for (int j = 1; j <= min(i, M - 1); j++)
      for (int k = 0; k <= i; k++)
        dp[i][j] =
            (dp[i][j] + ((fact[j] * B[k][j]) % MOD) * ch[i - k][j]) % MOD;
  cin >> t;
  while (t--) {
    cin >> n >> m;
    cout << dp[n][m] << '\n';
  }
  return 0;
}

### Prompt

Generate 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;
constexpr int N = 1000 + 10;
constexpr int M = 70;
constexpr int MOD = 1e9 + 7;
long long t, n, m, fact[N], B[N][N], ch[N][N], dp[N][N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  fact[0] = 1;
  for (int i = 1; i < N; i++) fact[i] = (fact[i - 1] * i) % MOD;
  for (int i = 0; i < N; i++) {
    for (int j = 0; j <= i; j++) {
      if (!j || i == j) {
        ch[i][j] = 1;
        continue;
      }
      ch[i][j] = (ch[i - 1][j] + ch[i - 1][j - 1]) % MOD;
    }
  }
  B[0][0] = B[0][1] = 1;
  for (int i = 1; i < N; i++)
    for (int j = N - 1; j >= i; j--)
      for (int k = 1; k < M; k++) B[j][k] = (B[j][k] + B[j - i][k - 1]) % MOD;
  for (int i = 1; i < N; i++)
    for (int j = 1; j <= min(i, M - 1); j++)
      for (int k = 0; k <= i; k++)
        dp[i][j] =
            (dp[i][j] + ((fact[j] * B[k][j]) % MOD) * ch[i - k][j]) % MOD;
  cin >> t;
  while (t--) {
    cin >> n >> m;
    cout << dp[n][m] << '\n';
  }
  return 0;
}

```