ZD. Subarray Distinct Values
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Constraints:

  • $$$1 \le k \le n \le 2 \cdot 10^5$$$
  • $$$1 \le x_i \le 10^9$$$
Output

Print one integer: the number of subarrays.

Example
Input
5 2
1 2 3 1 1
Output
10