Concatenated Multiples

You are given an array of n integers \(A_1,A_2,\dots,A_n\). You are allowed to pick two distinct elements \(A_i\) and \(A_j\) (with \(i \neq j\)) and concatenate their decimal representations in order (i.e. forming either \(A_iA_j\) or \(A_jA_i\)). Note that even if \(A_i=A_j\) in value, exchanging the order is considered different. For example, concatenating 12 and 345 may yield either 12345 or 34512.

Your task is to count how many ways to choose and order two different numbers so that the resulting integer is divisible by a given integer \(K\). The concatenated integer is formed as follows:

[ \text{result} = A_i \times 10^{d(A_j)} + A_j, ]

where \(d(A_j)\) denotes the number of digits of \(A_j\).

Input Constraints: It is guaranteed that the numbers and \(K\) are such that the answer fits in a 64-bit signed integer.

inputFormat

The first line contains two integers \(n\) and \(K\) separated by a space.

The second line contains \(n\) positive integers \(A_1, A_2, \dots, A_n\) separated by spaces.

outputFormat

Output a single integer, which is the number of valid concatenation ways such that the resulting integer is divisible by \(K\).

sample

4 3
1 2 3 4

4