| <p>You are given two integers <strong>N</strong> and <strong>K</strong>, 1 ≤ <strong>N</strong> ≤ 1000, 1 ≤ <strong>K</strong> ≤ 10<sup>9</sup>. | |
| Your task is to calculate how many distinct trees with <strong>N</strong> vertices there are with each vertex colored with one of <strong>K</strong> 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.</p> | |
| <h2>Input</h2> | |
| <p>The first line contains a single integer <strong>T</strong>, <strong>T</strong> ≤ 20. <strong>T</strong> test cases follow, where each test case consists of two integers: <strong>N</strong> and <strong>K</strong>.</p> | |
| <h2>Output</h2> | |
| <p>Output one single line with the number of colored trees. | |
| Since this number might be very big, output it modulo <strong>1,000,000,007</strong>.</p> | |
| <h2>Examples</h2> | |
| <img src="https://fbcdn-dragon-a.akamaihd.net/cfs-ak-ash3/676523/506/293813004081038_-/tmp-/IV3SsS" /> | |