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 N, x;
  cin >> N >> x;
  vector<long> A(N), data(N);
  for (int i = 0; i < N; i++) {
    cin >> A.at(i);
    data.at(i) = A.at(i);
  }
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      if (i > j) {
        data.at(i) = min(data.at(i), data.at(j) + x * (i - j));
      } else {
        data.at(i) = min(data.at(i), data.at(j) + x * ((j - i) % N));
      }
    }
  }
  long ans = 0;
  for (int i = 0; i < N; i++) ans += data.at(i);
  cout << ans << endl;
  return 0;
}
