1250 - Check If It Is a Good Array.

Hard

Given an array nums of positive integers. Your task is to select some subset of nums, multiply each element by an integer and add all these numbers. The array is said to be **good **if you can obtain a sum of 1 from the array by any possible subset and multiplicand.

Return True if the array is **good **otherwise return False.

Example 1:

Input: nums = 12,5,7,23

Output: true

Explanation: Pick numbers 5 and 7. 5\*3 + 7\*(-2) = 1

Example 2:

Input: nums = 29,6,10

Output: true

Explanation: Pick numbers 29, 6 and 10. 29\*1 + 6\*(-3) + 10\*(-1) = 1

Example 3:

Input: nums = 3,6

Output: false

Constraints:

• 1 <= nums.length <= 10^5

• 1 <= nums[i] <= 10^9