Problem2888--Beautiful Pairs of Numbers

2888: Beautiful Pairs of Numbers

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Source/Category

 
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