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 main() {
  cin.sync_with_stdio(false);
  cin.tie(0);
  long long n, x;
  cin >> n >> x;
  long long a[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  int length[n];
  fill(length, length + n, 0);
  int mx = 0;
  int t = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (a[(i + j) % n] > a[i] + x * j) {
        a[(i + j) % n] = a[i] + x * j;
        length[(i + j) % n] = j;
        if (j > mx) {
          mx = j;
          t = (i + j) % n;
        }
      }
    }
  }
  long long ans = (long long)mx * x;
  int tmp = t;
  while (true) {
    int l = length[tmp];
    tmp -= l;
    if (tmp < 0) tmp += n;
    ans += a[tmp] * (long long)(l + 1);
    tmp--;
    if (tmp < 0) tmp += n;
    if (tmp == t) break;
  }
  cout << ans << "\n";
  return 0;
}
