The Environmental Protection Agency (EPA) receives daily sensor readings along a river.

Each reading is an integer:

1 ... 10^5 represents a specific contaminant type. 0 represents a missing/unreadable measurement.

The EPA wants to identify continuous sequences of days containing exactly k distinct contaminants.

A 0 reading is a wildcard/missing value and does not count as a distinct contaminant.

Given an array of n readings, return the total number of contiguous subarrays containing exactly k distinct non-zero values.

Input Format

First line:

n k

Second line:

nums[0] nums[1] ... nums[n-1]

Constraints

1 ≤ n ≤ 2 × 10^4

0 ≤ nums[i] ≤ 10^5

1 ≤ k ≤ n

0 does not contribute to the distinct-contaminant count.

Output Format

Print one integer:

number of contiguous subarrays containing exactly k distinct non-zero values

Test Case 1

6 2

3 0 1 2 1 0

Answer:

9

Some valid windows include:

[3,0,1]

[3,0,1,2]

[0,1,2]

[1,2]

[1,2,1]

[2,1,0] ...

All have exactly 2 distinct non-zero values.

Test Case 2

5 1

0 4 0 4 0

Every non-empty subarray containing 4 has exactly one distinct contaminant.

Number of valid subarrays:

12

Output:

12