Problem: You are given the array a consisting of n elements and the integer k ≤ n.

You want to obtain at least k equal elements in the array a. In one move, you can make one of the following two operations:

  * Take one of the minimum elements of the array and increase its value by one (more formally, if the minimum value of a is mn then you choose such index i that a_i = mn and set a_i := a_i + 1); 
  * take one of the maximum elements of the array and decrease its value by one (more formally, if the maximum value of a is mx then you choose such index i that a_i = mx and set a_i := a_i - 1). 



Your task is to calculate the minimum number of moves required to obtain at least k equal elements in the array.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a and the required number of equal elements.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Print one integer — the minimum number of moves required to obtain at least k equal elements in the array.

Examples

Input


6 5
1 2 2 4 2 3


Output


3


Input


7 5
3 3 2 1 1 1 3


Output


4

Solution (in PYTHON3):

Solution:
def main():
    import sys
    input=sys.stdin.readline
    n,k=map(int,input().split())
    A=list(map(int,input().split()))
    A.sort()
    A.append(0)
    l1=[0]*n
    for i in range(1,n):
        l1[i]=l1[i-1]+(A[i]-A[i-1])*i 
    l2=[0]*n
    for i in range(1,n):
        l2[n-i-1]=l2[n-i]+(A[n-i]-A[n-i-1])*i 
    ans=float("INF")
    c=1
    for i in range(n):
        if A[i+1]==A[i]:
            c+=1
        else:
            c1=i-c+1
            c2=n-i-1
            if c>=k:
                ans=0
            elif c+c1>=k or c+c2>=k:
                if c+c1>=k:
                	ans=min(ans,l1[i]-c-c1+k)
                if c+c2>=k:
                	ans=min(ans,l2[i]-c-c2+k)
            else:
                ans=min(ans,l1[i]+l2[i]-n+k)
            c=1
    print(ans)
if __name__ == '__main__':
    main()