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>
//#include<atcoder/all>
using namespace std;
//using namespace atcoder;
int main(){
  int n,x;
  cin>>n>>x;
  vector<int> a(n);
  vector<int> m(n);
  int64_t mi=0;
  for(int i=0;i<n;i++){
    cin>>a.at(i);
    m.at(i)=a.at(i);
    mi+=m.at(i);
  }
  for(int i=1;i<n;i++){
    int64_t s=(int64_t)x*i;
    for(int j=0;j<n;j++){
      m.at(j)=min(m.at(j),a.at((j-i+n)%n));
      s+=m.at(j);
    }
    mi=min(s,mi);
  }
  cout<<mi<<endl;
}