🧩 Construct the Minimum Bitwise Array II

Difficulty: Easy
Topics: Bit Manipulation, Arrays

📘 Problem Statement

You are given an array nums consisting of n prime integers.

Your task is to construct an array ans of length n such that for every index i:

ans[i] | (ans[i] + 1) === nums[i]

🎯 Objective

• For each index i, find the minimum possible value of ans[i] that satisfies the condition.
• If no such value exists, set ans[i] = -1.

✨ Examples

Example 1

Input

nums = [2, 3, 5, 7]

Output

[-1, 1, 4, 3]

Explanation

• 2 → ❌ No value satisfies the condition → -1
• 3 → 1 | 2 = 3
• 5 → 4 | 5 = 5
• 7 → 3 | 4 = 7

Example 2

Input

nums = [11, 13, 31]

Output

[9, 12, 15]

Explanation

• 9 | 10 = 11
• 12 | 13 = 13
• 15 | 16 = 31

🧠 Key Insight

• The expression x | (x + 1) turns all trailing zeros into ones.
• If nums[i] is even, it is impossible to form it using x | (x + 1).
• For odd primes, the smallest valid x can be found by clearing the lowest set bit.

📌 Constraints

• 1 ≤ nums.length ≤ 100
• 2 ≤ nums[i] ≤ 1000
• nums[i] is always a prime number

🚀 Summary

✔ Odd primes → usually possible
❌ Even numbers → impossible
🎯 Goal → minimize ans[i]

Happy Coding! 💻🔥