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

Remember that a subarray is a contiguous section of the array.

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 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

Input

5 3
1 2 1 3 2

Output

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]~