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