You will be given an array A of size N and also given Q queries. In each query you will be given a number K. You have to print two number S₁ and S₂. Where S₁ is the sum of all the elements that are strictly less than K, and S₂ is the sum of all the elements that are strictly greater than K.

Input

Input starts with an integer T (1 <= T <= 20), denoting the number of test cases. Each test case starts with two integers N (1 <= N <= 10⁵) and Q (1 <= Q <= 10⁵). N denotes the number of elements in the array and Q is the number of queries. The next line contain N integers A₀, A₁, A₂, ..., A_N-1 (0 <= A_i <= 10⁹). Then the next line contains Q integers K (0 <= K <= 10⁹). For each K you have to print S₁and S₂.

Output

For each test case print "Case X:" (without quotes) where X is the running test case number. Then next Q lines consist of S₁ and S₂ for every given K in the current test case. Where S₁ is the sum of all the elements that are strictly less than K, and S₂ is the sum of all the elements that are strictly greater than K.

Sample

Input
2
10 5
5 1 0 8 1 13 34 21 3 2
1 2 3 4 35
7 2
6 24 120 1 720 2 1
1 23
Output
Case 1:
0 86
2 84
4 81
7 81
88 0
Case 2:
0 872
10 864