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>
int min[2010]={0};
int a[2010],pos[2010];
int main(void){
	int n,x,max=0;
	scanf("%d%d",&n,&x);
	long long ans=0;
	for (int i=1;i<=n;i++) 
	{scanf("%d",&a[i]);min[i]=a[i];ans+=a[i];}
	for (int d=1;d<n;d++){
		long long sum=1ll*d*x;
		for (int i=1;i<=n;i++){
			int j=i-d<=0?i-d+n:i-d;
			if (a[j]<min[i]){
				min[i]=a[j];
			}
			sum+=min[i];
		}
		if (sum<ans) ans=sum;
	}
	printf("%lld\n",ans);
}