You are given two integers N and K, 1 ≤ N ≤ 1000, 1 ≤ K ≤ 109. Your task is to calculate how many distinct trees with N vertices there are with each vertex colored with one of K colors. Multiple vertices can have the same color, and not all colors need to be used. Two trees t1 and t2 are considered identical if there exists a bijective function f from vertices of t1 to vertices of t2 such that each vertex x in t1 is colored the same as f(x) in t2 and each pair of vertices x, y in t1 is connected by an edge if and only if f(x) and f(y) are connected by an edge in t2. A bijective function is a function that is both one-to-one and onto, meaning that f(x) = f(y) if and only if x = y, and for every vertex y in t2, there exists x in t1, such that f(x) = y.
Input
The first line contains a single integer T, T ≤ 20. T test cases follow, where each test case consists of two integers: N and K.
Output
Output one single line with the number of colored trees. Since this number might be very big, output it modulo 1,000,000,007.
Examples
