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[20002];
long long s[20002];
int main() {
  long long n, m;
  cin >> n >> m;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  long long ans = 1000000007;
  for (long long i = 0; i < n; i++) {
    long long sum = i * m;
    for (long long j = 0; j < n; j++) {
      long long now = j + i;
      if (now >= n) {
        now -= n;
      }
      if (s[j] == 0) {
        s[j] = a[now];
      } else if (s[j] > a[now]) {
        s[j] = a[now];
      }
      sum += s[j];
    }
    ans = min(sum, ans);
  }
  cout << ans;
  return 0;
}
