class Solution:
    def findMedianSortedArrays(self, nums1: list[int], nums2: list[int]) -> float:
        if len(nums1) <= len(nums2):
            A, B = nums1, nums2
        else:
            A, B = nums2, nums1
        half_total = (len(A) + len(B)) // 2
        lo, hi = 0, len(A)
        while True:
            i = (lo + hi) // 2
            j = half_total - i
            Aleft = A[i - 1] if i > 0 else float("-inf")
            Aright = A[i] if i < len(A) else float("inf")
            Bleft = B[j - 1] if j > 0 else float("-inf")
            Bright = B[j] if j < len(B) else float("inf")
            if Aleft > Bright:
                hi = i - 1
            elif Bleft > Aright:
                lo = i + 1
            else:
                if (len(A) + len(B)) % 2 != 0:
                    return min(Aright, Bright)
                else:
                    return (max(Aleft, Bleft) + min(Aright, Bright)) / 2