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;
int read() {
  int x = 0, flag = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') flag = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = (x << 3) + (x << 1) + (ch - 0x30);
    ch = getchar();
  }
  return flag * x;
}
int n, a[5009], b[5009], m;
long long ans;
int main() {
  n = read(), m = read();
  for (register int i = (1), i_end_ = (n); i <= i_end_; ++i)
    a[i] = read(), b[i] = a[i], ans += a[i];
  for (register int i = (1), i_end_ = (n - 1); i <= i_end_; ++i) {
    long long _buff = 0;
    for (register int j = (1), j_end_ = (n); j <= j_end_; ++j) {
      int tmp = (j - (i + 1) + n) % n + 1;
      b[j] = min(b[j], a[tmp]);
      _buff += b[j];
    }
    ans = min(_buff + i * m, ans);
  }
  printf("%lld\n", ans);
  return 0;
}
