Kth Smallest Product of Two Sorted Arrays

You are given two sorted 0-indexed integer arrays nums1 and nums2 as well as an integer k, return the kth (1-based) smallest product of nums1[i] * nums2[j] where 0 <= i < nums1.length and 0 <= j < nums2.length.

Example 1:

Input: nums1 = [2,5], nums2 = [3,4], k = 2

Output: 8

Explanation: The 2 smallest products are:

• nums1[0] * nums2[0] = 2 * 3 = 6
• nums1[0] * nums2[1] = 2 * 4 = 8
  The 2-nd smallest product is 8.

Example 2:

Input: nums1 = [-4,-2,0,3], nums2 = [2,4], k = 6

Output: 0

Explanation: The 6 smallest products are:

• nums1[0] * nums2[1] = (-4) * 4 = -16
• nums1[0] * nums2[0] = (-4) * 2 = -8
• nums1[1] * nums2[1] = (-2) * 4 = -8
• nums1[1] * nums2[0] = (-2) * 2 = -4
• nums1[2] * nums2[0] = 0 * 2 = 0
• nums1[2] * nums2[1] = 0 * 4 = 0
  The 6-th smallest product is 0.

Example 3:

Input: nums1 = [-2,-1,0,1,2], nums2 = [-3,-1,2,4,5], k = 3

Output: -6

Explanation: The 3 smallest products are:
- nums1[0] * nums2[4] = (-2) * 5 = -10
- nums1[0] * nums2[3] = (-2) * 4 = -8
- nums1[4] * nums2[0] = 2 * (-3) = -6
The 3-rd smallest product is -6.

Constraints:

• 1 <= nums1.length, nums2.length <= 50,000
• -100,000 <= nums1[i], nums2[j] <= 100,000
• 1 <= k <= nums1.length * nums2.length
• nums1 and nums2 are sorted.

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