You are given an integer array nums and an integer k.

A subarray is a contiguous, non-empty part of the array.

Return the number of subarrays of nums that contain exactly k distinct values.

Examples

Example 1

Input: nums = [1,2,1,2,3], k = 2
Output: 7
Explanation: The subarrays with exactly 2 distinct values are [1,2], [2,1],
[1,2], [2,3], [1,2,1], [2,1,2], and [1,2,1,2].

Example 2

Input: nums = [1,2,1,3,4], k = 3
Output: 3
Explanation: The subarrays with exactly 3 distinct values are [1,2,1,3],
[2,1,3], and [1,3,4].