BANSTAND - Colored Development
There are N unique colors in the universe, numbered from 1 to N. George Michael wants to create a rainbow using these colors. The rainbow will consist of exactly M layers. For each layer, George Michael selects a color uniformly randomly from the N colors and colors the layer with it. George Michael wonders what will be the expected number of distinct colors in the rainbow after all the layers are colored in this way.
1 ≤ T ≤ 10
1 ≤ N, M ≤ 2 * 105
InputThe first line of the input contains an integer T, denoting the number of test cases. Each of the next T lines will contain two integers, N and M.
OutputFor each test case, print the case number and the expected number of distinct colors in the rainbow after all the layers are colored. Formally, let the expected number of distinct colors be an irreducible fraction P / Q. Then you need to print (P * Q-1) modulo 1000000007, where Q-1 is the modular inverse of Q modulo 1000000007. You may safely assume that there will be a unique modular inverse of Q modulo 1000000007.
3 1 1 2 2 4 2
Case 1: 1 Case 2: 500000005 Case 3: 750000007
ChallengeToo easy? Try the harder version here: