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 long long read() {
  long long x = 0;
  char ch = getchar();
  while (ch < '0' || '9' < ch) ch = getchar();
  while ('0' <= ch && ch <= '9') x = x * 10 + (ch ^ 48), ch = getchar();
  return x;
}
const int N = 2009;
long long n, x, ans;
long long a[N];
inline void chkmin(long long &a, long long b) {
  if (a > b) a = b;
}
int main() {
  n = read();
  x = read();
  for (int i = 1; i <= n; i++) ans += (a[i] = read());
  long long sum = 0;
  for (int i = 1; i <= n; i++) {
    sum += x;
    long long tot = 0;
    for (int j = 1; j <= n; j++) {
      chkmin(a[j], a[(j - i >= 1) ? (j - i) : (j - i + n)]);
      tot += a[j];
    }
    chkmin(ans, tot + sum);
  }
  printf("%lld\n", ans);
  return 0;
}
