There are N
workers. The i
th worker has a quality[i]
and a minimum wage expectation wage[i]
.
Now we want to hire exactly K
workers to form a paid group. When hiring a group of K workers, we must pay them according to the following rules:
 Every worker in the paid group should be paid in the ratio of their quality compared to other workers in the paid group.
 Every worker in the paid group must be paid at least their minimum wage expectation.
Return the least amount of money needed to form a paid group satisfying the above conditions.
Example 1:
Input: quality = [10,20,5], wage = [70,50,30], K = 2 Output: 105.00000 Explanation: We pay 70 to 0th worker and 35 to 2th worker.
Example 2:
Input: quality = [3,1,10,10,1], wage = [4,8,2,2,7], K = 3 Output: 30.66667 Explanation: We pay 4 to 0th worker, 13.33333 to 2th and 3th workers seperately.
Note:

1 <= K <= N <= 10000
, whereN = quality.length = wage.length
1 <= quality[i] <= 10000
1 <= wage[i] <= 10000
 Answers within
10^5
of the correct answer will be considered correct.