You are given an array with N integers, and another integer M. You have to find the number of consecutive subsequences which are divisible by M.
For example, let N = 4,the array be {2, 1, 4, 3} and M = 4.
The consecutive subsequences are {2}, {2 1}, {2 1 4}, {2 1 4 3}, {1}, {1 4}, {1 4 3}, {4}, {4 3}, {3}. Of these 10 'consecutive subsequences', only two of them adds up to a figure that is a multiple of 4 - {1 4 3}, {4}.
Input
Input starts with an integer T (≤ 10), denoting the number of test cases.
Each case contains two integers N (1 ≤ N ≤ 105) and M (1 ≤ M ≤ 105). The next line contains N space separated integers forming the array. Each of these integers will lie in the range [1, 105].
Output
For each case, print the case number and the total number of consecutive subsequences that are divisible by M.
Sample
| Sample Input | Sample Output |
|---|---|
2 4 4 2 1 4 3 6 3 1 2 3 4 5 6 | Case 1: 2 Case 2: 11 |
Notes
Dataset is huge. Use faster i/o methods.