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 200\,000~
~1 \le K \le 50\,000~
~1 \le a_i \le 1\,000\,000~

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