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 <iostream>
#include <algorithm>
#include <climits>
using namespace std;
using ll = long long;

int main(){
  ll n, x; cin >> n >> x;
  ll a[n+1], b[n+1];
  for(int i=1; i<=n; i++){
    cin >> a[i];
    b[i] = a[i];
  };

  ll ans = LLONG_MAX;
  for(int k=0; k<n; k++){
    ll tmp = 0;
    for(int i=1; i<=n; i++){
      int be = (i-k <= 0)? i-k+n: i-k;
      b[i] = min(b[i], a[be]);
      tmp += b[i];
    }
    ans = min(ans, tmp + k*x);
  }

  cout << ans << endl;

  return 0;
}
