The Alliance, which was at war with Collea, uses a highly convoluted method to encrypt their messages which involves signaling a long series of positive integers. Despite their best attempts, Collea was unable to effectively decrypt their messages. However, they have found out that a sequence of these signals might be an encrypted message if and only if the sum of the integers signalled is a multiple of $K$. The Alliance had just signalled $N$ integers. Help the Collean Armed Forces find how many continuous intervals of these signals might contain an encrypted message.

Constraints

$1\le N\le 200000$
$1\le K\le 50000$
$1\le a_i\le 1000000$

Input Specification

The first line contains two positive integers, $N$ and $K$.
The next line contains $N$ positive integers, the numbers $a_1,a_2,\dots ,a_N$.

Output Specification

Print one integer, the number of intervals of the signals whose elements sum to a multiple of $K$.

Sample Input

5 4
60 2 7 1 2

Sample Output

4