Given an integer array arr and an integer target.

Consider a function that calculates the bitwise AND of all elements in a contiguous subarray from index l to index r (inclusive), where $0 \leq l \leq r <$ arr.length.

Return the minimum absolute difference between the bitwise AND value of any contiguous subarray and target. In other words, find the minimum value of |( ext{arr}[l] ext{ \\& } ext{arr}[l + 1] ext{ \\& } \dots ext{ \\& } ext{arr}[r]) - ext{target}| across all valid pairs $(l, r)$.

Constraints:

• $1 \leq$ arr.length $\leq 10^5$

• $1 \leq$ arr[i] $\leq 10^6$

• $0 \leq$ target $\leq 10^7$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.