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

Example Output

10