Problem Description
Given an array of integers, perform atmost K operations so that the sum of elements of final array is minimum. An operation is defined as follows -
Consider any 1 element from the array, arr[i].
Replace arr[i] by floor(arr[i]/2).
Perform next operations on updated array.
The task is to minimize the sum after atmost K operations.
Constraints
1 <= N, K <= 10^5.
Input
First line contains two integers N and K representing size of array and maximum numbers of operations that can be performed on the array respectively.
Second line contains N space separated integers denoting the elements of the array, arr.
Output
Print a single integer denoting the minimum sum of the final array.
Time Limit
1
Examples
Example 1
Input
4 3
20 7 5 4
Output
17
Explanation
Operation 1 -> Select 20. Replace it by 10.
New array = [10, 7, 5, 4]
Operation 2 -> Select 10. Replace it by 5.
New array = [5, 7, 5, 4].
Operation 3 -> Select 7. Replace it by 3.
New array = [5,3,5,4].
Sum = 17.