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Time Limit: 1 s Memory Limit: 1024 MB Total points: 100

#6170. Convex Polygon Regular Partitioning Problem

The problem was used in the following contests:

2020 福建省队选拔赛 Day 2 (FJOI 2020 Day 2)

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

Regular Polygon Triangulation Problem: Given $n$ and $k$, find the number of ways to perform a $k$-angulation of a convex $nk-2(n-1)$-gon, modulo $10^9+7$.

Input

Each test case contains multiple queries.

The first line of the input contains two integers $n, k$.

Output

Output a single integer representing the sum of the answers for all queries.

Examples

Input 1

2 3
3 3
3 4

Output 1

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