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 n, x, arr[100000];
vector<pair<int, int>> v;
int main() {
  cin >> n >> x;
  for (int i = 1; i <= n; i++) cin >> arr[i];
  for (int i = n + 1; i <= 2 * n; i++) arr[i] = arr[i - n];
  int maxi = -INT_MAX, ans = 0, flag = 0;
  for (int j = 1; j <= n; j++) {
    int mini = INT_MAX;
    int cur = 0;
    if (arr[j] <= x) {
      ans += arr[j];
      continue;
    }
    for (int i = j + 1; i <= n + j - 1; i++) {
      int tutgac = abs(n - i + j);
      if (mini > tutgac * x + arr[i]) mini = tutgac * x + arr[i], cur = arr[i];
    }
    maxi = max(maxi, mini - cur);
    flag = 1;
    ans += cur;
  }
  if (flag == 0)
    cout << ans;
  else
    cout << maxi + ans;
}
