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[2005][2004];
int main() {
  long long n, m;
  long long i, j, k, flag, num[2006];
  scanf("%lld%lld", &n, &m);
  for (i = 1; i <= n; i++) scanf("%lld", &num[i]);
  for (i = 1; i <= n; i++) {
    a[i][0] = num[i];
    for (k = 1; k <= n - 1; k++) {
      flag = i - k;
      if (flag <= 0) flag = n + flag;
      a[i][k] = min(a[i][k - 1], num[flag]);
    }
  }
  long long minn = 123456789;
  for (i = 0; i <= n - 1; i++) {
    long long ans = 0;
    for (j = 1; j <= n; j++) {
      ans += a[j][i];
    }
    minn = min(minn, ans + m * i);
  }
  printf("%lld\n", minn);
  return 0;
}
