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.

Input

The 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.

Constraints

  • 1 ≤ T ≤ 10
  • 1 ≤ N, M ≤ 2 * 105
  • Output

    For 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.

    Sample Input

    3
    1 1
    2 2
    4 2
    
    
    

    Sample Output

    Case 1: 1
    Case 2: 500000005
    Case 3: 750000007
    
    

    Challenge

    Too easy? Try the harder version here:

    Development Colored


    Added by:sgtlaugh
    Date:2020-05-21
    Time limit:10s
    Source limit:50000B
    Memory limit:1536MB
    Cluster: Cube (Intel G860)
    Languages:All
    Resource:Own Problem, Used in 2019-2020 ACM-ICPC Asia Dhaka Regional Contest