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<bits/stdc++.h>
#define F(i,a,b) for(int i=(a);i<=(b);++i)
using namespace std;typedef long long ll;
int n,x;
int a[2001],b[2001];
ll Ans;
int main(){
	scanf("%d%d",&n,&x);
	F(i,1,n) scanf("%d",a+i), Ans+=a[i], b[i]=a[i];
	F(i,1,n-1){
		ll sum=0;
		swap(a,b);
		F(j,1,n) b[j]=min(b[j],a[(j+n-2)%n+1]), sum+=b[j];
		Ans=min(Ans,sum+(ll)i*x);
	} printf("%lld",Ans);
	return 0;
}