以下哪个代码片段可以正确实现在升序整数数组nums中查找第一个大于等于目标值target的元素的下标（即左边界查找），若不存在则返回数组长度，且不会出现索引越界或死循环问题？

def left_bound(nums, target):
    left, right = 0, len(nums)
    while left < right:
        mid = left + (right - left) // 2
        if nums[mid] >= target:
            right = mid
        else:
            left = mid + 1
    return left

def left_bound(nums, target):
    left, right = 0, len(nums)-1
    while left <= right:
        mid = (left + right) // 2
        if nums[mid] >= target:
            right = mid -1
        else:
            left = mid
    return left

def left_bound(nums, target):
    left, right = 0, len(nums)-1
    while left < right:
        mid = left + (right - left) // 2
        if nums[mid] >= target:
            right = mid
        else:
            left = mid
    return left

def left_bound(nums, target):
    left, right = 0, len(nums)
    while left <= right:
        mid = left + (right - left) // 2
        if nums[mid] >= target:
            right = mid -1
        else:
            left = mid +1
    return left