K-Distinct Subarrays

Given an array $a$ of $n$ integers, count how many non-empty contiguous subarrays contain at least $k$ distinct values.

Input

The first line contains two integers $n$ and $k$.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$.

Output

Print a single integer: the number of non-empty contiguous subarrays that contain at least $k$ distinct values.

Constraints

• $1 \le k \le n \le 2 \cdot 10^5$
• $-10^9 \le a_i \le 10^9$

Example 1

5 3
1 2 1 3 2

5

Explanation

The subarrays with at least $3$ distinct values are:

• $[1, 2, 1, 3]$
• $[1, 2, 1, 3, 2]$
• $[2, 1, 3]$
• $[2, 1, 3, 2]$
• $[1, 3, 2]$