Return sorted values after quadratic transform

Problem

You are given a sorted integer array nums (non-decreasing order) and integers a, b, c that define a quadratic function:

$f(x) = ax^2 + bx + c$

Apply the function to every element in nums, producing an array res[i] = f(nums[i]). Return res in sorted (non-decreasing) order.

Input

• nums : sorted array of integers
• a , b , c : integers

Output

• A sorted array containing f(x) for each x in nums

Constraints

• 1 <= len(nums) <= 2 * 10^5
• -10^4 <= nums[i], a, b, c <= 10^4

Example

• Input: nums = [-4,-2,2,4], a = 1, b = 3, c = 5
• Output: [3,9,15,33]