Find smallest index sum of any pairs equal target

"""
Given two arrays, (say [1,3,5] and [2,4]) and a number target (say 7), assume we sort by the sum of any pair of elements from each array, return the smallest index.
In this example, the result is 3.
Pair, Sum, Index
(1,2), 3, 0
(1,4), 5, 1
(3,2), 5, 2
(3,4), 7, 3 <- result
(5,2), 7, 4
(5,4), 9, 5
"""

def binary_search(nums, target):
    """
    Find the largest index strictly smaller than a given number.

    Time complexity: O(log n)
    Space complexity: O(1)
    """
    start, end = 0, len(nums) - 1
    while start <= end:
        mid = start + (end - start) // 2
        if nums[mid] >= target:
            end = mid - 1
        else:
            start = mid + 1
    return end

def find_index(nums1, nums2, target):
    """
    Find the smallest index of pair sum equal to target from two sorted arrays.

    Time complexity: O(n log m), where n = len(nums1) and m = len(nums2)
    Space complexity: O(1) excluding input sorting
    """
    # Sort input arrays
    nums1.sort()
    nums2.sort()

    res = 0
    has_res = False

    # Iterate through nums1
    for num1 in nums1:
        # Find the largest index in nums2 where sum < target
        lb = binary_search(nums2, target - num1) + 1

        # Check if we found a pair sum equal to target
        if lb < len(nums2) and nums2[lb] == target - num1:
            has_res = True

        # Accumulate the index
        res += lb

    return res if has_res else -1

# Example usage
nums1 = [1, 3, 5]
nums2 = [2, 4]
target = 7
result = find_index(nums1, nums2, target)
print(f"Result: {result}")  # Expected output: 3