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>
#define ll long long
#define FOR(i,a,b) for(ll i=a;i<=b;i++)
using namespace std;
const int N=2003;
ll a[N],b[N],x,ans=0;
ll n,m;
int main()
{
	  
	  cin>>n>>x;
	  FOR(i,1,n)
	    cin>>a[i],ans+=a[i],b[i]=a[i];
	  FOR(i,1,n-1)
	  {
	  	ll sum=0;
	    FOR(j,1,n)
		  {
		       ll k=(j-i>0)?j-i:j-i+n;
			   if(a[k] < b[j]) sum+=a[k],b[j]=a[k];
			   else sum+=b[j];
		  }    
		 sum+=i*x;
	//	 cout<<sum<<endl;
		 ans=min(ans,sum); 
	  }
	  cout<<ans;
 	  return 0;
}