Subarrays with Distinct Values

Given an array of n integers, you are asked to calculate the number of subarrays that have at most k distinct characters.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ ).

The next line contains n space-separated integers (1 ≤ ≤ ).

Output

The program should print the number of subarrays that have at most k distinct values.

Examples

Explanation

2, 3, 4, 2, 2, 2 3, 3 4, 4 2, 2 2, 4 2 2