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 int n, x, arr[2010], from[2010], max_x, current_x, cvp;
int main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> x;
  for (int i = 0; i < n; i++) cin >> arr[i];
  for (int i = 0; i < n; i++) from[i] = i;
  for (int i = 0; i < n; ++i) {
    current_x = 0;
    for (int j = (i < 1 ? n - 1 : i - 1); j != i; j--) {
      current_x++;
      if (current_x * x + arr[j] <
          arr[from[i]] + x * (from[i] <= i ? i - from[i] : n - from[i] + i)) {
        max_x = max(max_x, current_x);
        from[i] = j;
      }
      if (j == 0) j = n;
    }
  }
  for (int i = 0; i < n; ++i) {
    cvp += arr[from[i]];
  }
  cout << cvp + max_x * x;
  return 0;
}
