Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.




Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9

Input

The input is given from Standard Input in the following format:


N x
a_1 a_2 ... a_N


Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
#include<stdio.h>

long long nn[2000][2000];

int main(){
		int n,i,j;
		long long x,a[2000];
		scanf("%d%lld",&n,&x);
		for(i=0;i<n;i++)scanf("%lld",&a[i]);
		for(i=0;i<n;i++){
				nn[i][i]=a[i];
		}
		for(i=0;i<n;i++){
				for(j=0;j<n;j++){
						nn[i][j]=nn[i][i];
						if(i>j)nn[i][j]+=(n-i+j)*x;
						else nn[i][j]+=(j-i)*x;
				}
		}
		long long ans=0;
		for(i=0;i<n;i++){
				long long tmp=-1;
				for(j=0;j<n;j++){
					if(tmp==-1)tmp=n[j][i];
						if(tmp>nn[j][i])tmp=nn[j][i];
				}
				ans+=tmp;
		}
		printf("%lld\n",ans);
		return 0;
}