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 rep(i,n) for(long long int (i)=0;(i)<(int)(n);(i)++)
#define rrep(i,a,b) for(long long int i=(a);i<(b);i++)
#define rrrep(i,a,b) for(long long int i=(a);i>=(b);i--)
#define all(v) (v).begin(), (v).end()
#define pb(q) push_back(q)
#define Abs(a,b) max(a,b)-min(a,b)
#define YES(condition) if(condition){cout << "YES" << endl;}else{cout << "NO" << endl;}
#define Yes(condition) if(condition){cout << "Yes" << endl;}else{cout << "No" << endl;}
#define Cout(x) cout<<(x)<<endl
#define POSSIBLE(condition) if(condition){cout << "POSSIBLE" << endl;}else{cout << "IMPOSSIBLE" << endl;}
#define Possible(condition) if(condition){cout << "Possible" << endl;}else{cout << "Impossible" << endl;}
#define possible(condition) if(condition){cout << "possible" << endl;}else{cout << "impossible" << endl;}
#define Size(n) (n).size()

typedef long long ll;


using namespace std;

const int INF = 1e9,MOD = 1e9 + 7,ohara = 1e6;
const ll LINF = 1e18;


long long int n,cnt=0,ans=INF,a[ohara],b[ohara],c,d,cmp[ohara],cmpp,m,h,w,x,y,sum=0,pos,mi[2002][2002];
int dy[]={1,0,-1,0};
int dx[]={0,1,0,-1};
string alph("abcdefghijklmnopqrstuvwxyz"),s;
bool fl;
struct edge{int to,cost;};

//-------------------------↓↓↓↓↓↓------------------------

int main(void){
       cin.tie(0);
    ios::sync_with_stdio(false);

      
      cin>>n>>x;
      pos=0;
      rep(i,n){
        cin>>a[i];
        pos+=a[i]
        b[i]=INF;
      }
      rrep(i,n,2*n){
        a[i]=a[i-n];
      }
      rep(i,n){
        cnt=n-1;
        rrrep(j,i+n,i+1){
          mi[i][cnt--]=a[j];
        }
      }
    rrep(genzaiti,n,2*n){
        rrep(to,1,n){
          mi[genzaiti-n][to]=min(mi[genzaiti-n][to],mi[genzaiti-n][to-1]);
        }
      }
      cnt=0;
      rep(mahou,n){
        if(mahou==0)continue;
        rep(j,n){
          cnt=min(a[j],a[2*n-j]);
        }
        cnt+=mahou*x;
        ans=min(ans,cnt);
        cnt=0;
      }
      Cout(min(ans,pos));
   
      
      
      

       
return 0;
}
