Maximum Bitwise AND After Increment Operations - LeetCode Hard

You are given an integer array nums and two integers k and m.

You may perform at most k operations. In one operation, you may choose any index i and increase nums[i] by 1.

Return an integer denoting the maximum possible bitwise AND of any subset of size m after performing up to k operations optimally.

Example 1:

Input: nums = [3,1,2], k = 8, m = 2

Output: 6

Explanation:

We need a subset of size m = 2. Choose indices [0, 2].
Increase nums[0] = 3 to 6 using 3 operations, and increase nums[2] = 2 to 6 using 4 operations.
The total number of operations used is 7, which is not greater than k = 8.
The two chosen values become [6, 6], and their bitwise AND is 6, which is the maximum possible.

Example 2:

Input: nums = [1,2,8,4], k = 7, m = 3

Output: 4

Explanation:

We need a subset of size m = 3. Choose indices [0, 1, 3].
Increase nums[0] = 1 to 4 using 3 operations, increase nums[1] = 2 to 4 using 2 operations, and keep nums[3] = 4.
The total number of operations used is 5, which is not greater than k = 7.
The three chosen values become [4, 4, 4], and their bitwise AND is 4, which is the maximum possible.

Example 3:

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

Output: 2

Explanation:

We need a subset of size m = 2. Choose indices [0, 1].
Increase both values from 1 to 2 using 1 operation each.
The total number of operations used is 2, which is not greater than k = 3.
The two chosen values become [2, 2], and their bitwise AND is 2, which is the maximum possible.

Constraints:

3806. Maximum Bitwise AND After Increment Operations