You are given an array aa, consisting of nn positive integers.
Let‘s call a concatenation of numbers xx and yy the number that is obtained by writing down numbers xx and yy one right after another without changing the order. For example, a concatenation of numbers 1212 and 34563456 is a number 123456123456.
Count the number of ordered pairs of positions (i,j)(i,j) (i≠ji≠j) in array aa such that the concatenation of aiai and ajaj is divisible by kk.
Input
The first line contains two integers nn and kk (1≤n≤2?1051≤n≤2?105, 2≤k≤1092≤k≤109).
The second line contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤1091≤ai≤109).
Output
Print a single integer — the number of ordered pairs of positions (i,j)(i,j) (i≠ji≠j) in array aa such that the concatenation of aiai and ajaj is divisible by kk.
Examples
input
Copy
6 11 45 1 10 12 11 7
output
Copy
7
input
Copy
4 2 2 78 4 10
output
Copy
12
input
Copy
5 2 3 7 19 3 3
output
Copy
0
Note
In the first example pairs (1,2)(1,2), (1,3)(1,3), (2,3)(2,3), (3,1)(3,1), (3,4)(3,4), (4,2)(4,2), (4,3)(4,3) suffice. They produce numbers 451451, 45104510, 110110, 10451045, 10121012, 121121, 12101210, respectively, each of them is divisible by 1111.
In the second example all n(n?1)n(n?1) pairs suffice.
