You are given an integer array nums.

For any permutation perm of nums, an array power of size $15$ is defined such that for each index i from $0$ to $14$, power[i] represents the length of the longest prefix of perm where every element has the bit at position $(14 - i)$ set to $1$.

Return the lexicographically largest power array that can be obtained by choosing an optimal permutation perm.

An array a is lexicographically larger than an array b of the same length if, at the first index where they differ, array a contains a value strictly greater than the corresponding value in array b.

Constraints:

• $1 \leq$ nums.length $\leq 5 imes 10^4$

• $0 \leq$ nums[i] $< 2^{15}$

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