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>
using namespace std;
typedef long long ll;
const int N=4010;
int n;ll x,a[N],Min[N][N];
int main()
{
	cin>>n>>x;
	for (int i=1;i<=n;i++) cin>>a[i],a[i+n]=a[i];
	for (int l=1;l<=n*2;l++){
		Min[l][l]=a[l];
		for (int r=l+1;r<=n*2;r++) Min[l][r]=min(Min[l][r-1],a[r]);
	}
	ll ans=1e16;
	for (int k=0;k<n;k++){//使用k次+1操作
		ll cost=k*x;
		for (int i=n+1;i<=n*2;i++) cost+=Min[i-k][i];
		ans=min(ans,cost);
	}
	cout<<ans<<endl;
	return 0;
}