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;
long long a[2010], N, X, D[2010][2010];
int main() {
  int i, j;
  long long hap = LONG_LONG_MAX;
  cin >> N >> X;
  for (i = 1; i <= N; i++) cin >> a[i];
  for (i = 1; i <= N; i++) D[i][i] = a[i];
  for (i = 1; i <= N - 1; i++) {
    for (j = 1; j <= N; j++) {
      D[j][(j + i - 1 + N) % N + 1] =
          min(min(D[j][(j + i - 2 + N) % N + 1] + X + a[j],
                  D[(j - 1) == 0 ? N : (j - 1)][(j + i - 3 + N) % N + 1] + X +
                      a[(j + i - 1 + N) % N + 1]),
              min(D[j][(j + i - 2 + N) % N + 1] + a[(j + i - 1 + N) % N + 1],
                  D[j % N + 1][(j + i - 1 + N) % N + 1] + a[j]));
    }
  }
  hap = D[1][N];
  for (i = 2; i <= N; i++) {
    hap = min(hap, D[i][i - 1]);
  }
  cout << hap << endl;
}
