Count Multiples in a Stream

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given n (possibly negative or zero) integers and positive integer k, count how many are divisible by k. Process values as they are read without storing an array.

Input

Integers n and k, followed by exactly n integers.

Output

One integer: the number of values satisfying x % k == 0.

Subtasks

• Subtask 1 (20%): $1\le n\le5$, $1\le k\le5$, $|x|\le10$.
• Subtask 2 (30%): $1\le n\le100$, $1\le k\le1000$, $|x|\le1000$.
• Subtask 3 (50%): $1\le n\le10000$, $1\le k\le10^6$, $|x|\le10^6$.

Examples

Example 1

Input

5 3
3 6 -9 2 0

Output

4

Explanation

3, 6, -9 and 0 are divisible by 3; 2 is not.

Example 2

Input

1 1
-7

Output

1

Explanation

Every integer is divisible by 1.