Given a sequence of positive integers, count all contiguous subsequences (sometimes called substrings, in contrast to subsequences, which may leave out elements) the sum of which is divisible by a given number. These subsequences may overlap. For example, the sequence (see sample input)
The first line of the input consists of an integer c (1 <= c <= 200), the number of test cases. Then follow two lines per test case.
Each test case starts with a line consisting of two integers d (1 <= d <= 1 000 000) and n (1 <= n <= 50 000), the divisor of the sum of the subsequences and the length of the sequence, respectively. The second line of a test case contains the elements of the sequence, which are integers between 1 and 1 000 000 000, inclusively.
For each test case, print a single line consisting of a single integer, the number of contiguous subsequences the sum of which is divisible by d.
2 7 3 1 2 3 4 8 2 1 2 1 1 2 1 2
0 6