Subarray Distinct Values

• Time limit: 1.00 s
• Memory limit: 512 MB

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