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 int long long

int N,X;
int a[2002];

int memo[2002][2002];
int mmm(int i, int n) {
  return (memo[i][n] = (
    n==1 ? a[i] : min(memo[(i+N-1)%N][n-1], a[i])
//    n==1 ? a[i] : min(memo[i][n-1], a[(i-n+1+N)%N])
  ));
}

signed main() {
  cin>>N>>X;
  for(int i=0;i<N;i++)cin>>a[i];
  int q=1LL<<60;
  for(int t=0;t<N;t++){
    int r=0;
    for(int i=0;i<N;i++){
      r+=mmm((N+i-t)%N, t+1);
    }
    q=min(q,r+X*t);
  }
  cout<<q<<endl;
}