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, n) for (int i = 0; i < (int)(n); i++)
int main(){
  int n;
  cin >> n;
  long long x;
  cin >> x;
  long long k[n];
  rep(i,n)cin >> k[i];
  long long mi[n][n];
  rep(i,n){
    mi[i][0]=k[i];
  }
  rep(i,n-1){
    rep(j,n){
      mi[j][i+1]=min(mi[j][i],k[(j-i-1+n)%n]);
    }
  }
  long long ans=100000000000000;
  rep(i,n){
    long long t=0;
    rep(j,n)t+=mi[j][i];
    ans=min(ans,t+i*x);
  }
  cout << ans << endl;
} 
