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_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  long long x;
  cin >> n >> x;
  vector<long long> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  vector<long long> cant(n, 0);
  vector<long long> lon(n, 0);
  for (int i = 0; i < n; ++i) {
    int cont = 1;
    long long mejor = a[i];
    long long index = i;
    long long tam = 0;
    for (int j = (i + 1) % n; j != i; j = (j + 1) % n) {
      int k = (j > i) ? j - i : j + n - i;
      long long current = x * k + a[j];
      if (current < mejor) {
        mejor = current;
        index = j;
        tam = k;
      }
    }
    cant[index]++;
    lon[index] = max(lon[index], tam);
  }
  long long resp = 0;
  for (int i = 0; i < n; ++i) {
    resp += (cant[i] * a[i] + x * lon[i]);
  }
  cout << resp << '\n';
}
