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;
int N, x;
int a[2000];
int main(void) {
  cin >> N >> x;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
  }
  long long ans = 0;
  long long changing_max = 0;
  for (int catching = 0; catching < N; catching++) {
    long long catch_cost = a[catching];
    long long changing = 0;
    int catch_slime = -1;
    for (int current_ind = 1; current_ind < N; current_ind++) {
      int current = (catching - current_ind + N) % N;
      changing += x;
      if (catch_cost > changing + a[current]) {
        catch_cost = changing + a[current];
        catch_slime = current;
      }
    }
    if (catch_cost == a[catching]) {
      ans += catch_cost;
    } else {
      changing_max = max(changing_max, changing);
      ans += a[catch_slime];
    }
  }
  cout << ans + changing_max << endl;
  return 0;
}
