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