"""
Given an integer array nums and an integer k, return true if nums has a continuous subarray of size at least two whose elements sum up to a multiple of k, or false otherwise.

An integer x is a multiple of k if there exists an integer n such that x = n * k. 0 is always a multiple of k.

Example 1:
Input: nums = [23,2,4,6,7], k = 6
Output: true
Explanation: [2, 4] is a continuous subarray of size 2 whose elements sum up to 6.

Example 2:
Input: nums = [23,2,6,4,7], k = 6
Output: true
Explanation: [23, 2, 6, 4, 7] is an continuous subarray of size 5 whose elements sum up to 42.
42 is a multiple of 6 because 42 = 7 * 6 and 7 is an integer.

Example 3:
Input: nums = [23,2,6,4,7], k = 13
Output: false


Constraints:
1 <= nums.length <= 105
0 <= nums[i] <= 109
0 <= sum(nums[i]) <= 231 - 1
1 <= k <= 231 - 1
"""
from typing import List


class ContinuousSubarraySum:
    def checkSubarraySum(self, nums: List[int], k: int) -> bool:
        first_occur = {0: -1}
        total = 0
        for i, n in enumerate(nums):
            total = (total + n) % k
            if total in first_occur:
                if i - first_occur[total] > 1:
                    return True
            else:
                first_occur[total] = i
        return False
