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You are given an array of n integers, nums, where there are at most 50 unique values in the array. You are also given an array of m customer order quantities, quantity, where quantity[i] is the amount of integers the ith customer ordered. Determine if it is possible to distribute nums such that:

  • The ith customer gets exactly quantity[i] integers,
  • The integers the ith customer gets are all equal, and
  • Every customer is satisfied.

Return true if it is possible to distribute nums according to the above conditions.

 

Example 1:

Input: nums = [1,2,3,4], quantity = [2]
Output: false
Explanation: The 0th customer cannot be given two different integers.

Example 2:

Input: nums = [1,2,3,3], quantity = [2]
Output: true
Explanation: The 0th customer is given [3,3]. The integers [1,2] are not used.

Example 3:

Input: nums = [1,1,2,2], quantity = [2,2]
Output: true
Explanation: The 0th customer is given [1,1], and the 1st customer is given [2,2].

Example 4:

Input: nums = [1,1,2,3], quantity = [2,2]
Output: false
Explanation: Although the 0th customer could be given [1,1], the 1st customer cannot be satisfied.

Example 5:

Input: nums = [1,1,1,1,1], quantity = [2,3]
Output: true
Explanation: The 0th customer is given [1,1], and the 1st customer is given [1,1,1].

 

Constraints:

  • n == nums.length
  • 1 <= n <= 105
  • 1 <= nums[i] <= 1000
  • m == quantity.length
  • 1 <= m <= 10
  • 1 <= quantity[i] <= 105
  • There are at most 50 unique values in nums.

class Solution { public boolean canDistribute(int[] nums, int[] quantity) { } }