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 N = 2005;
int n, x, m, a[N];
long long ans, sum;
int main() {
  cin >> n >> x, ans = 0;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  sort(a + 1, a + 1 + n);
  ans = 1ll * a[1] * n + 1ll * x * (n - 1);
  for (int i = 1; i <= n; ++i) {
    if (a[i] > x) {
      ans = min(ans, sum + 1ll * a[1] * (n - i + 1) + 1ll * x * (n - i + 1));
      break;
    } else
      sum += a[i];
  }
  if (a[n] <= x) ans = min(ans, sum);
  cout << ans << endl;
  return 0;
}
