Count Subarrays with Exactly K Odd Numbers

You are given an array of n integers and an integer k. Your task is to count the number of contiguous subarrays (i.e., continuous segments of the array) that contain exactly k odd numbers.

The problem can be formalized as follows: Given an array \(nums\) and an integer \(k\), find the number of subarrays \(nums[i \ldots j]\) that satisfy:

[ \text{count}_{odd}(nums[i \ldots j]) = k ]

where \(\text{count}_{odd}(\cdot)\) counts the number of odd integers in the subarray.

Example:

Input: 5 3
       1 1 2 1 1
Output: 2

In this example, there are exactly 2 contiguous subarrays with 3 odd numbers.

inputFormat

The first line contains two integers n and k, where n is the number of elements in the array, and k is the target number of odd numbers.

The second line contains n integers separated by spaces representing the elements of the array.

outputFormat

Output a single integer, representing the number of contiguous subarrays that contain exactly k odd numbers.

## sample

5 3
1 1 2 1 1

2