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 maxn = 1e5;
int cmp(int x, int y) { return x > y; }
int main() {
  long long ans = 0;
  int n, x;
  int time[maxn + 5], vis[maxn + 5];
  cin >> n >> x;
  for (int i = 0; i < n; i++) cin >> time[i];
  int pos = 0, c = 0, c1 = 0, ite = 0;
  bool lit = false;
  for (int i = 0; i < n; i = (i + 1) % n) {
    if (lit && i == 0) break;
    if (!vis[i] && lit && time[i] > x) {
      vis[i] = 1;
      ans += pos;
      c++;
    }
    if (time[i] < x + pos) {
      if (c > ite) ite = c;
      pos = time[i];
      lit = true;
      c = 0;
    }
  }
  if (c + c1 > ite) ite = c + c1;
  ans += ite * x;
  for (int i = 0; i < n; i++)
    if (!vis[i]) ans += time[i];
  cout << ans << endl;
  return 0;
}
