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;
const int inf = 2e9;
const long long ll_inf = 1e17;
const int mod = 1e9 + 7;
const long double eps = 1e-10;
long long a[2010];
long long b[2010];
long long c[2010];
int main() {
  int n, x;
  cin >> n >> x;
  for (int i = (0); i < (n); i++) {
    cin >> a[i];
    b[i] = a[i];
    c[i] = a[i];
  }
  int move = 0;
  for (int i = (0); i < (n); i++) {
    int m = 0;
    for (int j = (0); j < (n); j++) {
      int idx = (n + i - j) % n;
      if (b[i] > b[idx] + j * x) {
        b[i] = b[idx] + j * x;
        c[i] = b[idx];
        m = j;
      }
    }
    move = max(move, m);
  }
  long long ans = 0;
  for (int i = (0); i < (n); i++) {
    ans += c[i];
  }
  ans += x * move;
  cout << ans << endl;
  return 0;
}
