#include <bits/stdc++.h>
using namespace std;
const int N = 1010, p = 1e9 + 7;
int T, n, k, inv[N], fac[N], cnt[N][N];
inline int P(int x, int y) { return 1ll * fac[x] * inv[x - y] % p; }
int main() {
  fac[0] = 1;
  for (int i = 1; i < N; ++i) fac[i] = 1ll * fac[i - 1] * i % p;
  inv[0] = inv[1] = 1;
  for (int i = 2; i < N; ++i) inv[i] = 1ll * inv[p % i] * (p - p / i) % p;
  for (int i = 3; i < N; ++i) inv[i] = 1ll * inv[i - 1] * inv[i] % p;
  cnt[1][1] = 1;
  for (int i = 1; i <= 1000; ++i)
    for (int j = i + 1; j <= 1000; ++j)
      cnt[i][j] = (cnt[i][j - i] + cnt[i - 1][j - i]) % p;
  scanf("%d", &T);
  while (T-- > 0) {
    scanf("%d%d", &n, &k);
    int ans = 0;
    for (int i = (k * k - k) / 2; i + k <= n; ++i)
      ans = (ans + 1ll * P(n - i, k) * cnt[k][i + k] % p) % p;
    printf("%d\n", (ans + p) % p);
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 = 1010, p = 1e9 + 7;
int T, n, k, inv[N], fac[N], cnt[N][N];
inline int P(int x, int y) { return 1ll * fac[x] * inv[x - y] % p; }
int main() {
  fac[0] = 1;
  for (int i = 1; i < N; ++i) fac[i] = 1ll * fac[i - 1] * i % p;
  inv[0] = inv[1] = 1;
  for (int i = 2; i < N; ++i) inv[i] = 1ll * inv[p % i] * (p - p / i) % p;
  for (int i = 3; i < N; ++i) inv[i] = 1ll * inv[i - 1] * inv[i] % p;
  cnt[1][1] = 1;
  for (int i = 1; i <= 1000; ++i)
    for (int j = i + 1; j <= 1000; ++j)
      cnt[i][j] = (cnt[i][j - i] + cnt[i - 1][j - i]) % p;
  scanf("%d", &T);
  while (T-- > 0) {
    scanf("%d%d", &n, &k);
    int ans = 0;
    for (int i = (k * k - k) / 2; i + k <= n; ++i)
      ans = (ans + 1ll * P(n - i, k) * cnt[k][i + k] % p) % p;
    printf("%d\n", (ans + p) % p);
  }
  return 0;
}

```