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>
int main() {
  int i, j;
  int n, x;
  int a[2003] = {0};
  scanf("%d %d", &n, &x);
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  unsigned long long int ans = 0;
  int max = 0;
  for (i = 0; i < n; i++) {
    unsigned long long int min = 1000000000 * (long long int)n + 1000000005;
    int minj = 0;
    int maxj = 0;
    for (j = 0; j < n; j++) {
      unsigned long long int time =
          (long long int)a[j] +
          (long long int)x * ((i - j) < 0 ? i - j + n : i - j);
      if (time < min) {
        min = time;
        minj = j;
        maxj = (i - j) < 0 ? i - j + n : i - j;
      }
    }
    ans += a[minj];
    if (maxj > max) max = maxj;
  }
  ans += x * max;
  printf("%lld", ans);
}
