Distinct Values Subarrays II

Given an array of n integers, your task is to calculate the number of subarrays that have at most k distinct values.

Input

The first input line has two integers n and k. The next line has n integers x_1,x_2,\dots,x_n: the contents of the array.

Output

Print one integer: the number of subarrays.

Constraints

$1 \le k \le n \le 2 \cdot 10^5$

$1 \le x_i \le 10^9$

Example

Input

5 2
1 2 3 1 1

Output

10