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::sync_with_stdio(false);
  int n, x;
  while (cin >> n >> x) {
    int a[2010], k = 0, b[2010], temp;
    long long sum = 0;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
    }
    for (int i = 1; i <= n; i++) {
      int max = a[i];
      b[i] = a[i];
      for (int j = 1; j <= n - 1; j++) {
        if (i - j < 1)
          temp = i - j + n;
        else
          temp = i - j;
        if ((a[temp] + j * x) < max) {
          max = a[temp] + j * x;
          b[i] = a[temp];
          k = k > j ? k : j;
        }
      }
    }
    for (int i = 1; i <= n; i++) sum += b[i];
    sum += k * x;
    cout << sum << endl;
  }
  return 0;
}
