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>
#include<algorithm>
using namespace std;
int c[110000];
int d[110000];
int main(){
	int a,b;scanf("%d%d",&a,&b);
	for(int i=0;i<a;i++)scanf("%d",c+i);
	for(int i=0;i<a;i++)d[i]=c[i];
	long long ret=0;
	for(int i=0;i<a;i++)ret+=c[i];
	for(int i=1;i<a;i++){
		for(int j=0;j<a;j++){
			d[j]=min(d[j],c[(j+a-i)%a]);
		}
		long long tmp=(long long)b*i;
		for(int j=0;j<a;j++)tmp+=d[j];
		ret=min(ret,tmp);
	}
	printf("%lld\n",ret);
}