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][2010];
int main() {
  long long n, x;
  cin >> n >> x;
  for (int i = 0; i < (int)(n); i++) cin >> A[0][i + 1];
  for (int i = 1; i < n; i++) {
    A[i][1] = A[i - 1][n];
    for (int j = 2; j <= n; j++) {
      A[i][j] = A[i - 1][j - 1];
    }
  }
  long long ma = 0, ans = 0;
  for (long long j = 1; j <= n; j++) {
    long long mi = A[0][j], y = 0, tmp = A[0][j];
    for (long long i = 1; i < n; i++) {
      if (mi > A[i][j] + x * i) {
        mi = A[i][j] + x * i;
        tmp = A[i][j];
        y = i;
      }
    }
    ans += tmp;
    ma = max(ma, y);
  }
  ans += ma * x;
  cout << ans << endl;
  return 0;
}
