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

Your task is to partition nums into k non-empty subarrays. For each subarray, compute the bitwise XOR of all its elements.

Return the minimum possible value of the maximum XOR among these k subarrays.

 

Example 1:

Input: nums = [1,2,3], k = 2

Output: 1

Explanation:

The optimal partition is [1] and [2, 3].

The maximum XOR among the subarrays is 1, which is the minimum possible.

Example 2:

Input: nums = [2,3,3,2], k = 3

Output: 2

Explanation:

The optimal partition is [2], [3, 3], and [2].

The maximum XOR among the subarrays is 2, which is the minimum possible.

Example 3:

Input: nums = [1,1,2,3,1], k = 2

Output: 0

Explanation:

The optimal partition is [1, 1] and [2, 3, 1].

The maximum XOR among the subarrays is 0, which is the minimum possible.

 

Constraints: