"""
You are given two positive integer arrays nums and numsDivide. You can delete any number of elements from nums.
Return the minimum number of deletions such that the smallest element in nums divides all the elements of numsDivide. If this is not possible, return -1.
Note that an integer x divides y if y % x == 0.

Example 1:
Input: nums = [2,3,2,4,3], numsDivide = [9,6,9,3,15]
Output: 2
Explanation:
The smallest element in [2,3,2,4,3] is 2, which does not divide all the elements of numsDivide.
We use 2 deletions to delete the elements in nums that are equal to 2 which makes nums = [3,4,3].
The smallest element in [3,4,3] is 3, which divides all the elements of numsDivide.
It can be shown that 2 is the minimum number of deletions needed.

Example 2:
Input: nums = [4,3,6], numsDivide = [8,2,6,10]
Output: -1
Explanation:
We want the smallest element in nums to divide all the elements of numsDivide.
There is no way to delete elements from nums to allow this.

Constraints:
1 <= nums.length, numsDivide.length <= 105
1 <= nums[i], numsDivide[i] <= 109

hint:
1 How can we find an integer x that divides all the elements of numsDivide?
2 Will finding GCD (Greatest Common Divisor) help here?
"""
from functools import reduce
from math import gcd
from typing import List


class Solution:
    def minOperations(self, nums: List[int], numsDivide: List[int]) -> int:
        g = reduce(gcd, numsDivide)
        for i, n in enumerate(sorted(nums)):
            if g % n == 0:
                return i
            if n > g:
                break
        return -1