def insert_log(lst, item):
    placed = True

    low = 0
    top = len(lst)
    mid =  top // 2

    while placed:
        index = lst[mid]

        if index == item:
            placed = False
            lst.insert(index, item)

        if lst[mid] > item > lst[mid-1]:

            placed = False
            lst.insert(mid, item)

        elif index > item:
            top = mid
            mid = (low + mid) // 2

        elif index < item:
            low = mid
            mid = low + ((top - low) // 2)
    return lst