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;
#define mod 1000000007
#define INF 1e9

int main(){
    ll N,x;
    cin>>N>>x;
    
    ll a[N],c[N];
    
    ll ans=0;
    for(int i=0;i<N;i++){
        cin>>a[i];
        c[i]=a[i];
        ans+=a[i];
    }
    for(ll t=1;t<N;t++){
        ll cost=t*x;
        for(int i=0;i<N;i++){
            c[i]=min(c[i],a[(i+N-t)%N]);
            cost+=c[i];
        }
        ans=min(ans,cost);
    }
    cout<<ans<<endl;
}