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>
long long b[2000][2000];
int main() {
  int n, i, j, k;
  long long x, a[2000], ans = -1;
  scanf("%d%lld", &n, &x);
  for (i = 0; i < n; i++) {
    scanf("%lld", &a[i]);
    b[0][i] = a[i];
  }
  for (k = 0; k < n; k++) {
    long long tmp = k * x;
    if (k > 0) {
      for (i = 0; i < n; i++) {
        if (i >= k)
          b[k][i] = ((b[k - 1][i]) < (b[k - 1][i - k]) ? (b[k - 1][i])
                                                       : (b[k - 1][i - k]));
        else
          b[k][i] = ((b[k - 1][i]) < (b[0][n - k + i]) ? (b[k - 1][i])
                                                       : (b[0][n - k + i]));
      }
    }
    for (i = 0; i < n; i++) tmp += b[k][i];
    if (ans == -1) ans = tmp;
    ans = ((ans) < (tmp) ? (ans) : (tmp));
  }
  printf("%lld\n", ans);
  return 0;
}
