You are given two sorted $0$-indexed integer arrays nums1 and nums2, along with an integer k.

Consider all possible products formed by nums1[i] * nums2[j], where i ranges over all valid indices of nums1 and j ranges over all valid indices of nums2. Return the $k^{th}$ smallest product among all such pairs, using $1$-based indexing.

Note: Both nums1 and nums2 are sorted in non-decreasing order. The arrays may contain negative numbers and zero, so the products can be negative, zero, or positive.

Constraints:

• $1 \leq$ nums1.length, nums2.length $\leq 5 \times 10^4$

• $-10^5 \leq$ nums1[i], nums2[j] $\leq 10^5$

• $1 \leq$ k $\leq$ nums1.length $\times$ nums2.length

• nums1 and nums2 are sorted in non-decreasing order

The key insight is that we cannot enumerate all products explicitly since there can be up to $2.5 \times 10^9$ ...