1770 - Maximum Score from Performing Multiplication Operations.

Medium

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 <code>i^th</code> 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

• <code>1 <= m <= 10³</code>

• <code>m <= n <= 10⁵</code>

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