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 MOD = 1000000007;
int main() {
  std::ios_base::sync_with_stdio(false);
  int n;
  long long x;
  cin >> n >> x;
  std::vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  long long ans = 0LL;
  int max_d = 0;
  for (int i = 0; i < n; i++) {
    long long mi = a[i];
    int origin = i;
    int d = 0;
    for (int j = 0; j < n; j++) {
      if (i == j) continue;
      if (j > i && a[j] + x * (n - (j - i)) < mi) {
        origin = j;
        d = n - (j - i);
        mi = a[j] + x * (n - (j - i));
      } else if (j < i && a[j] + x * (i - j) < mi) {
        origin = j;
        d = i - j;
        mi = a[j] + x * (i - j);
      }
    }
    if (origin == i) {
      ans += a[i];
    } else {
      ans += a[origin];
    }
    max_d = max(max_d, d);
  }
  cout << ans + max_d * x << endl;
  return 0;
}
