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Subarrays with distinct integers!


Problem Description

Given an array A of positive integers,call a (contiguous,not necessarily distinct) subarray of A good if the number of different integers in that subarray is exactly B.

(For example: [1, 2, 3, 1, 2] has 3 different integers 1, 2 and 3)

Return the number of good subarrays of A.



Problem Constraints

1 <= |A| <= 40000

1 <= A[i] <= |A|

1 <= B <= |A|



Input Format

The first argument given is the integer array A.

The second argument given is an integer B.



Output Format

Return an integer denoting the number of good subarrays of A.



Example Input

Input 1:

 A = [1, 2, 1, 2, 3]
 B = 2

Input 2:

 A = [1, 2, 1, 3, 4]
 B = 3



Example Output

Output 1:

 7

Output 2:

 3



Example Explanation

Explanation 1:

  Subarrays formed with exactly 2 different integers: [1, 2], [2, 1], [1, 2], [2, 3], [1, 2, 1], [2, 1, 2], [1, 2, 1, 2].

Explanation 2:

  Subarrays formed with exactly 3 different integers: [1, 2, 1, 3], [2, 1, 3], [1, 3, 4].



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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