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 int long long
#define r(i,n) for(int i=0;i<n;i++)
using namespace std;
int n,x,dp[2009][2009],ans,tmp[2009];
signed main(){
    cin>>n>>x;
    r(i,n)cin>>dp[0][i],ans+=dp[0][i];
    for(int i=1;i<n;i++){
        int s=0;
        r(j,n)dp[i][j]=dp[i-1][j];
        r(j,n){
            tmp[j]=min(dp[i][j],dp[i][(j-1+n)%n]);
            s+=tmp[j];
        }
        r(j,n)dp[i][j]=tmp[j];
        ans=min(ans,s+x*i);
    }
    cout<<ans<<endl;
}
