Quadratic Application

You are given a list of integers nums sorted in ascending order, and integers a, b, and c. Apply the following function for each number x in nums: \(ax^2 + bx + c\) and return the resulting list in ascending order.

This should be done in \(\mathcal{O}(n)\) time.

Constraints

• n ≤ 100,000 where n is the length of nums

https://binarysearch.com/problems/Quadratic-Application

Examples

Example 1

Input

• nums = [-2, 3]
• a = 1
• b = -3
• c = 2

Output

• answer = [2, 12]

Explanation

We have

• nums[0] = 1*-2**2 + -3*-2 + 2 = 4 + 6 + 2 = 12
• nums[1] = 1*3**2 + -3*3 + 2 = 9 + -9 + 2 = 2

After we sort [12, 2], we get [2, 12]

Solution