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;
long long a[4444], x;
int main() {
  int n;
  scanf("%d%lld", &n, &x);
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
    a[i + n] = a[i];
  }
  int flag = 0;
  for (int i = n + 1; i <= n + n; i++) {
    if (a[i] > x) {
      long long t = a[i];
      int idx = i - 1;
      long long mx = a[i];
      for (int j = 1; j < n; j++, idx--) {
        t = min(t, a[idx] + (i - idx) * x);
        if (a[idx] + (i - idx) * x <= t) {
          t = a[idx] + (i - idx) * x;
          flag = max(flag, i - idx);
          mx = max(mx, a[idx]);
        }
      }
      ans += mx;
    } else {
      ans += a[i];
    }
  }
  printf("%lld", ans + flag * x);
  return 0;
}
