A12038 | Concatenated Multiples

You are given an array $a$ , consisting of $n$ positive integers.

Let's call a concatenation of numbers $x$ and $y$ the number that is obtained by writing down numbers $x$ and $y$ one right after another without changing the order. For example, a concatenation of numbers $12$ and $3456$ is a number $123456$ .

Count the number of ordered pairs of positions $(i,j)$ ( $i≠j$ ) in array $a$ such that the concatenation of $a_{i}$ and $a_{j}$ is divisible by $k$ .

The first line contains two integers $n$ and $k$ ( $1<=n<=2·10^{5}$ , $2<=k<=10^{9}$ ).

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ).

Print a single integer — the number of ordered pairs of positions $(i,j)$ ( $i≠j$ ) in array $a$ such that the concatenation of $a_{i}$ and $a_{j}$ is divisible by $k$ .