The sequence of integer pairs $(*a*_{1}, *b*_{1}), (*a*_{2}, *b*_{2}), ..., (*a*_{*k*}, *b*_{*k*})$ is beautiful, if the following statements are fulfilled:

• $1 ≤ *a*_{1} ≤ *b*_{1} < *a*_{2} ≤ *b*_{2} < ... < *a*_{*k*} ≤ *b*_{*k*} ≤ *n*$, where $*n*$ is a given positive integer;
• all numbers $*b*_{1} - *a*_{1}$, $*b*_{2} - *a*_{2}$, $...$, $*b*_{*k*} - *a*_{*k*}$ 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 $1000000007$ $(10^{9} + 7)$.

Input

The first line contains integer $*t*$ ($1 ≤ *t* ≤  2·10^{5}$) — 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 $1000000007$ $(10^{9} + 7)$. Print the answers to the tests in the order in which the tests are given in the input.

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.