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;
  cin >> n >> x;
  vector<long long> a(n, 0);
  for (int i = 0; i < int(n); ++i) {
    cin >> a[i];
  }
  vector<long long> min_a(n, 0);
  vector<long long> ini_a(n, 0);
  vector<long long> step_a(n, 0);
  for (int i = 0; i < int(n); ++i) {
    min_a[i] = a[i];
    ini_a[i] = a[i];
    for (int j = i - 1; j != i; j--) {
      if (j < 0) {
        j = n - 1;
      }
      long long tmp_s = i >= j ? (i - j) : (i + n) - j;
      long long tmp_m = tmp_s * x + a[j];
      if (tmp_m < min_a[i]) {
        min_a[i] = tmp_m;
        ini_a[i] = a[j];
        step_a[i] = tmp_s;
      }
      if (j <= 0) {
        j = n;
      }
    }
  }
  long long res = 0;
  for (int i = 0; i < int(n); ++i) {
    res += ini_a[i];
  }
  sort(step_a.begin(), step_a.end());
  res += step_a[n - 1] * x;
  cout << res << endl;
  return 0;
}
