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;
typedef long long ll;
int main() {
  ll n,x;
  cin >> n >> x;
  vector<ll> a(n), v(n);
  for(int i=0;i<n;i++) {
    cin >> a[i];
    v[i] = a[i];
  }

  ll ans = 1e9 * 2100;
  for(int k=0;k<n;k++) {
    ll k_ans = 0;
    for(int i=0;i<n;i++) {
      if(i-k < 0) {
        v[i] = min<ll>(v[i], a[n+i-k]);
      } else {
        v[i] = min<ll>(v[i], a[i-k]);
      }

      k_ans += v[i];
    }
    ans = min<ll>(ans, k_ans + k * x);
  }
  cout << ans << endl;


}