You are given an integer array nums and two integers cost1 and cost2. You are allowed to perform either of the following operations any number of times:
i from nums and increase nums[i] by 1 for a cost of cost1.i, j, from nums and increase nums[i] and nums[j] by 1 for a cost of cost2.Return the minimum cost required to make all elements in the array equal.
\n\nSince the answer may be very large, return it modulo 109 + 7.
\n
Example 1:
\n\nInput: nums = [4,1], cost1 = 5, cost2 = 2
\n\nOutput: 15
\n\nExplanation:
\n\nThe following operations can be performed to make the values equal:
\n\nnums[1] by 1 for a cost of 5. nums becomes [4,2].nums[1] by 1 for a cost of 5. nums becomes [4,3].nums[1] by 1 for a cost of 5. nums becomes [4,4].The total cost is 15.
\nExample 2:
\n\nInput: nums = [2,3,3,3,5], cost1 = 2, cost2 = 1
\n\nOutput: 6
\n\nExplanation:
\n\nThe following operations can be performed to make the values equal:
\n\nnums[0] and nums[1] by 1 for a cost of 1. nums becomes [3,4,3,3,5].nums[0] and nums[2] by 1 for a cost of 1. nums becomes [4,4,4,3,5].nums[0] and nums[3] by 1 for a cost of 1. nums becomes [5,4,4,4,5].nums[1] and nums[2] by 1 for a cost of 1. nums becomes [5,5,5,4,5].nums[3] by 1 for a cost of 2. nums becomes [5,5,5,5,5].The total cost is 6.
\nExample 3:
\n\nInput: nums = [3,5,3], cost1 = 1, cost2 = 3
\n\nOutput: 4
\n\nExplanation:
\n\nThe following operations can be performed to make the values equal:
\n\nnums[0] by 1 for a cost of 1. nums becomes [4,5,3].nums[0] by 1 for a cost of 1. nums becomes [5,5,3].nums[2] by 1 for a cost of 1. nums becomes [5,5,4].nums[2] by 1 for a cost of 1. nums becomes [5,5,5].The total cost is 4.
\n\n
Constraints:
\n\n1 <= nums.length <= 1051 <= nums[i] <= 1061 <= cost1 <= 1061 <= cost2 <= 106cost2 > cost1 * 2, we should just use cost1 to change all the values to the maximum one.",
"Otherwise, it's optimal to choose the smallest two values and use cost2 to increase both of them.",
"Since the maximum value is known, calculate the required increases to equalize all values, instead of naively simulating the operations.",
"There are not a lot of candidates for the maximum; we can try all of them and choose which uses the minimum number of operations."
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