Distinct Values Subarrays II

Given an array of $nn$ integers, your task is to calculate the number of subarrays that have at most $kk$ distinct values.

Input

The first input line has two integers $nn$ and $kk$.

The next line has $nn$ integers $x_1,x_2,\dots ,x_{n}x\_1,x\_2,\backslash dots,x\_n$: the contents of the array.

Output

Print one integer: the number of subarrays.