3312 - Sorted GCD Pair Queries.

Hard

You are given an integer array nums of length n and an integer array queries.

Let gcdPairs denote an array obtained by calculating the GCD of all possible pairs (nums[i], nums[j]), where 0 <= i < j < n, and then sorting these values in ascending order.

For each query queries[i], you need to find the element at index queries[i] in gcdPairs.

Return an integer array answer, where answer[i] is the value at gcdPairs[queries[i]] for each query.

The term gcd(a, b) denotes the greatest common divisor of a and b.

Example 1:

Input: nums = 2,3,4, queries = 0,2,2

Output: 1,2,2

Explanation:

gcdPairs = [gcd(nums[0], nums[1]), gcd(nums[0], nums[2]), gcd(nums[1], nums[2])] = [1, 2, 1].

After sorting in ascending order, gcdPairs = [1, 1, 2].

So, the answer is [gcdPairs[queries[0]], gcdPairs[queries[1]], gcdPairs[queries[2]]] = [1, 2, 2].

Example 2:

Input: nums = 4,4,2,1, queries = 5,3,1,0

Output: 4,2,1,1

Explanation:

gcdPairs sorted in ascending order is [1, 1, 1, 2, 2, 4].

Example 3:

Input: nums = 2,2, queries = 0,0

Output: 2,2

Explanation:

gcdPairs = [2].

Constraints:

• <code>2 <= n == nums.length <= 10⁵</code>

• <code>1 <= numsi<= 5 * 10⁴</code>

• <code>1 <= queries.length <= 10⁵</code>

• 0 <= queries[i] < n * (n - 1) / 2