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 LL long long
#define MAX 2005
using namespace std;
int n,x;
int a[MAX],mn[MAX];
LL calc(int t){
	for (int i=0;i<n;i++) mn[i]=min(mn[i],a[(i-t+n)%n]);
	LL tans=0;
	for (int i=0;i<n;i++) tans+=mn[i];
	return tans;
}
int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n>>x;
	for (int i=0;i<n;i++) cin>>a[i];
	for (int i=0;i<n;i++) mn[i]=1e9+10;
	LL ans=1e18+10;
	for (int i=0;i<n;i++)
	  ans=min(ans,1ll*x*i+calc(i));
	cout<<ans<<'\n';
	return 0;
}