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Minimum Number of K Consecutive Bit Flips

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

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

A k-bit flip is choosing a subarray of length k from nums and simultaneously changing every 0 in the subarray to 1, and every 1 in the subarray to 0.

Return the minimum number of k-bit flips required so that there is no 0 in the array. If it is not possible, return -1.

A subarray is a contiguous part of an array.

Minimum Number of K Consecutive Bit Flips diagram

Example 1

Input: nums = [0,1,0], k = 1

Output: 2

Explanation: Flip nums[0], then flip nums[2].

Example 2

Input: nums = [1,1,0], k = 2

Output: -1

Explanation: No matter how we flip subarrays of size 2, we cannot make the array become [1,1,1].

Example 3

Input: nums = [0,0,0,1,0,1,1,0], k = 3

Output: 3

Explanation: Flip nums[0],nums[1],nums[2]: nums becomes [1,1,1,1,0,1,1,0] Flip nums[4],nums[5],nums[6]: nums becomes [1,1,1,1,1,0,0,0] Flip nums[5],nums[6],nums[7]: nums becomes [1,1,1,1,1,1,1,1]

Constraints

  • 1 <= nums.length <= 10^5
  • 1 <= k <= nums.length

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