Beautiful Pairs of Numbers

3000ms

262144K

Description:

The sequence of integer pairs (a₁, b₁), (a₂, b₂), ..., (a_k, b_k) is beautiful, if the following statements are fulfilled:

1 ≤ a₁ ≤ b₁ < a₂ ≤ b₂ < ... < a_k ≤ b_k ≤ n, where n is a given positive integer;
all numbers b₁ - a₁, b₂ - a₂, ..., b_k - a_k 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.

Sample Input:

Sample Output:

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.

Informação

Provedor Codeforces

Código CF403D