# https://leetcode.com/problems/count-the-hidden-sequences

from typing import List

class Solution:
    def numberOfArrays(self, differences: List[int], lower: int, upper: int) -> int:
        total = 0
        min_sum = 0
        max_sum = 0
        for diff in differences:
            total += diff
            min_sum = min(min_sum, total)
            max_sum = max(max_sum, total)

        min_start = lower - min_sum
        max_start = upper - max_sum

        return max(0, max_start - min_start + 1)