# LeetCode — Maximum score from performing multiplication operation

You are given two integer arrays `nums`

and `multipliers`

** **of size `n`

and `m`

respectively, where `n >= m`

. The arrays are **1-indexed**.

You begin with a score of `0`

. You want to perform **exactly** `m`

operations. On the `ith`

operation **(1-indexed)**, you will:

- Choose one integer
`x`

from**either the start or the end**of the array`nums`

. - Add
`multipliers[i] * x`

to your score. - Remove
`x`

from the array`nums`

.

Return *the **maximum** score after performing *`m`

*operations.*

**Example 1:**

**Input:** nums = [1,2,3], multipliers = [3,2,1]

**Output:** 14

**Explanation:** An optimal solution is as follows:

- Choose from the end, [1,2,**3**], adding 3 * 3 = 9 to the score.

- Choose from the end, [1,**2**], adding 2 * 2 = 4 to the score.

- Choose from the end, [**1**], adding 1 * 1 = 1 to the score.

The total score is 9 + 4 + 1 = 14.

**Example 2:**

**Input:** nums = [-5,-3,-3,-2,7,1], multipliers = [-10,-5,3,4,6]

**Output:** 102

**Explanation: **An optimal solution is as follows:

- Choose from the start, [**-5**,-3,-3,-2,7,1], adding -5 * -10 = 50 to the score.

- Choose from the start, [**-3**,-3,-2,7,1], adding -3 * -5 = 15 to the score.

- Choose from the start, [**-3**,-2,7,1], adding -3 * 3 = -9 to the score.

- Choose from the end, [-2,7,**1**], adding 1 * 4 = 4 to the score.

- Choose from the end, [-2,**7**], adding 7 * 6 = 42 to the score.

The total score is 50 + 15 - 9 + 4 + 42 = 102.

**Constraints:**

`n == nums.length`

`m == multipliers.length`

`1 <= m <= 103`

`m <= n <= 105`

`-1000 <= nums[i], multipliers[i] <= 1000`

Solution:

Time complexity: **O(n²)**

Space complexity: **O(n²)**