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;
  bool t = false;
  char ch = getchar();
  while ((ch < '0' || ch > '9') && ch != '-') ch = getchar();
  if (ch == '-') t = true, ch = getchar();
  while (ch <= '9' && ch >= '0') x = x * 10 + ch - 48, ch = getchar();
  return t ? -x : x;
}
int n, K, a[2020];
int mn[2020];
long long ans = 1e18;
int main() {
  n = read();
  K = read();
  for (int i = 1; i <= n; ++i) a[i] = mn[i] = read();
  for (int i = 0; i <= n; ++i) {
    for (int j = 1; j <= n; ++j)
      if (j - i > 0)
        mn[j] = min(mn[j], a[j - i]);
      else
        mn[j] = min(mn[j], a[j - i + n]);
    long long ret = 0;
    for (int j = 1; j <= n; ++j) ret += mn[j];
    ans = min(ans, ret + 1ll * K * i);
  }
  printf("%I64d\n", ans);
  return 0;
}
