Maximum Score Using Exactly K Pairs

Description

You are given two integer arrays nums1 and nums2 of lengths n and m respectively, and an integer k.

You must choose exactly k pairs of indices (i1, j1), (i2, j2), ..., (ik, jk) such that:

- 0 <= i1 < i2 < ... < ik < n

- 0 <= j1 < j2 < ... < jk < m

For each chosen pair (i, j), you gain a score of nums1[i] * nums2[j].

The total score is the sum of the products of all selected pairs.

Return an integer representing the maximum achievable total score.