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() {
  long long n, x, ans = 0, xc = 0;
  cin >> n >> x;
  vector<long long> a(n), b(n), cost(n, 1000000000);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (long long i = 0; i < n; i++) {
    long long xc0;
    for (long long j = 0; j < n; j++) {
      if (i >= j && cost[i] >= (i - j) * x + a[j]) {
        cost[i] = (i - j) * x + a[j];
        b[i] = a[j];
        xc0 = i - j;
      } else if (cost[i] >= (n - j + i) * x + a[j]) {
        cost[i] = (n - j + i) * x + a[j];
        b[i] = a[j];
        xc0 = n - j + i;
      }
    }
    xc = max(xc, xc0);
  }
  for (int i = 0; i < n; i++) {
    ans += b[i];
  }
  ans += xc * x;
  cout << ans << endl;
  return 0;
}
