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() {
  int n, x;
  cin >> n >> x;
  vector<int> a(n);
  vector<bool> b(n, false);
  for (int i = 0; i < n; ++i) cin >> a[i];
  long long ans = 0;
  int count = 0;
  bool flag = false;
  while (count < n) {
    flag = false;
    for (int i = 0; i < n; ++i) {
      if (a[i] <= x && b[i] == false) {
        ans += a[i];
        count++;
        b[i] = true;
        flag = true;
      }
    }
    if (flag == false) {
      ans += x;
      bool temp = b[n - 1];
      for (int i = 0; i < n - 1; ++i) {
        b[i + 1] = b[i];
      }
      b[0] = temp;
      int m = 2000000000;
      int k = 0;
      for (int i = 0; i < n; ++i) {
        if (a[i] < m && b[i] == false) {
          m = a[i];
          k = i;
        }
      }
      ans += a[k];
      b[k] = true;
      count++;
    }
  }
  cout << ans << endl;
  return 0;
}
