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(void) {
  int n, i, j;
  long long x;
  long long a[2200];
  while (scanf("%d%lld", &n, &x) == 2) {
    for (i = 1; i <= n; i++) scanf("%lld", &a[i]);
    long long ans = 0;
    int maxn = 0;
    int cnt = 0;
    for (i = 1; i <= n; i++) {
      long long t = a[i];
      int c = i;
      if (a[i] > x) {
        for (j = 1; j < i; j++) {
          if (a[j] + (i - j) * x < t) {
            t = (i - j) * x;
            c = j;
          }
        }
        for (j = i + 1; j <= n; j++) {
          if (a[j] + (n - j + i) * x < t) {
            t = (n - j + i) * x;
            c = j;
          }
        }
      }
      if (c < i) maxn = max(maxn, i - c);
      if (c > i) maxn = max(maxn, n - c + i);
      ans += a[c];
    }
    ans += maxn * x;
    cout << ans << endl;
  }
}
