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<iostream>
#include<cstdio>
#define ll long long
using namespace std;
ll n,x,a[2005],f[2005][2005],t,ans=1000000000000000;
ll min(ll x,ll y){
	return x<y?x:y;
}
int main(){
	scanf("%lld%lld",&n,&x);
	for(int i=1;i<=n;i++){
		scanf("%lld",&a[i]);
		f[i][0]=a[i];
	}
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++){
			t=i-j;
			if(t<=0) t=n+t;
			f[i][j]=min(f[i][j-1],a[t]);
		}
	for(int i=0;i<=n;i++){
		t=0;
		for(int j=1;j<=n;j++) t+=f[j][i];
		ans=min(ans,t+x*i);
	}
	printf("%lld\n",ans);
	return 0;
}