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;
void solve();
int main() {
  ios::sync_with_stdio(false);
  solve();
  return 0;
}
const int N = 2000;
pair<int, int> a[N];
int b[N];
void solve() {
  int n, x;
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    int v;
    cin >> v;
    a[i] = pair<int, int>(v, i);
    b[i] = v;
  }
  sort(a, a + n);
  long long res = LLONG_MAX;
  set<int> ids;
  for (int i = 0; i < n; i++) {
    long long cur_res = 0;
    int x_max = 0;
    ids.insert(a[i].second);
    int cur = *(--ids.end());
    for (int i : ids) {
      int d = i - cur;
      if (d <= 0) d += n;
      cur_res += d * b[i];
      x_max = max(x_max, d - 1);
      cur = i;
    }
    cur_res += x_max * x;
    res = min(res, cur_res);
  }
  cout << res << endl;
}
