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 main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  long long int a[3005], x, cnt = 0, ans = 0;
  pair<long long int, long long int> p[3005];
  cin >> x;
  for (int i = 0; i <= n - 1; i++)
    cin >> a[i], ans += a[i], p[i] = make_pair(a[i], i);
  sort(p, p + n);
  for (int ii = 1; ii <= n - 1; ii++) {
    int f[3005] = {0}, id = p[0].second;
    long long int s = 0;
    for (int i = 0; i <= ii - 1; i++) f[p[i].second] = 1;
    long long int lst, cnt = 0, mx = 0;
    int ptr = id;
    while (1) {
      if (f[ptr] == 1) {
        s += a[ptr];
        lst = a[ptr];
        cnt = 0;
      } else
        s += lst, cnt++;
      ptr++;
      ptr %= n;
      mx = max(mx, cnt);
      if (ptr == id) break;
    }
    ans = min(ans, s + cnt * x);
  }
  cout << ans;
  return 0;
}
