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;

#define rep(i,m,n) for(int i=m;i<n;i++)

typedef long long ll;

const ll inf=1000000000000000;

int main(){
   cin.tie(nullptr);
  ios::sync_with_stdio(false);
  
  ll n,x;
  cin >> n >> x;
  vector<ll> a(n),b(n);
  rep(i,0,n){
   cin >> a[i];
   b[i]=a[i];
  }
  ll res=inf;
  
  rep(k,0,n){
    ll sum=k*x;
   rep(i,0,n) {
     sum+=b[i];
     b[i]=min(b[i],a[(i-(k+1)+n)%n]);
   }
    res=min(res,sum);
    }
  cout << res << endl;
}