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;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch > '9' || ch < '0') ch == '-' && (f = 0) || (ch = getchar());
  while (ch <= '9' && ch >= '0')
    x = (x << 3) + (x << 1) + ch - '0', ch = getchar();
  return f ? x : -x;
}
long long a[2020], b[2020], x, ans;
int main(int argc, char const *argv[]) {
  int n = read();
  x = read();
  for (int i = 0; i < n; ++i) {
    a[i] = read();
  }
  int max_move = 0;
  for (int i = 0; i < n; ++i) {
    long long min_value = a[i];
    int step = 0;
    for (int len = 1; len < n; ++len) {
      int j = (i - len + n) % n;
      long long value = len * x + a[j];
      if (value < min_value) {
        min_value = value;
        step = len;
      }
    }
    ans += a[(i - step + n) % n];
    max_move = max(max_move, step);
  }
  ans += max_move * x;
  printf("%lld\n", ans);
  return 0;
}
