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 dp[2005];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, c, t, w, maxt = 0;
  long long a, s = 0, x, aux, ax;
  vector<long long> numb;
  cin >> n >> x;
  for (int i = 0; i < n; ++i) {
    cin >> a;
    numb.push_back(a);
  }
  for (int i = n - 1; i >= 0; i--) {
    if (numb[i] <= x) {
      w = i;
    } else {
      aux = numb[i];
      w = i;
      c = i - 1;
      t = 0;
      while (true) {
        t++;
        if (c == -1) {
          c = n - 1;
        }
        if (c == i) break;
        ax = (t * x) + numb[c];
        if (aux > ax) {
          aux = ax;
          w = c;
          maxt = max(maxt, t);
        }
        c--;
      }
    }
    dp[w]++;
  }
  for (int i = 0; i < n; ++i) {
    s += dp[i] * numb[i];
  }
  s += maxt * x;
  cout << s << endl;
  return 0;
}
