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 long long INF = 1e18;
const int inf = 1e9;
const int mod = 1e9 + 7;
const double EPS = (double)1e-9;
const double pi = acos(-1.0);
const int MAXN = 1e5 + 5;
int n;
long long a[2005], x, mn[4005][4005];
long long res = INF;
int main() {
  cin >> n >> x;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (int i = n + 1; i <= 2 * n; i++) {
    a[i] = a[i - n];
  }
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = i; j <= 2 * n; j++) {
      mn[i][j] = INF;
      if (i == j) mn[i][j] = a[i];
    }
  }
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = i + 1; j <= 2 * n; j++) {
      mn[i][j] = min(mn[i][j - 1], a[j]);
    }
  }
  for (int i = 0; i < n; i++) {
    long long val = i * x;
    for (int j = 1; j <= n; j++) {
      val += mn[j][j + i];
    }
    res = min(val, res);
  }
  cout << res;
  return 0;
}
