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 MOD = 1000000007;
signed main() {
  long long n, x;
  cin >> n >> x;
  long long a[2010];
  long long mina = LLONG_MAX / 2;
  long long p = 0;
  for (long long i = 0; i < (n); i++) {
    cin >> a[i];
    if (mina > a[i]) {
      mina = a[i];
      p = i;
    }
  }
  long long b[2010];
  for (long long i = 0; i < (n); i++) {
    if (i + p <= n - 1)
      b[i] = a[p + i];
    else
      b[i] = a[p + i - n];
  }
  long long ans = b[0] * n + x * (n - 1);
  long long c = b[0];
  for (long long i = 1; i <= n - 1; i++) {
    if (ans > ans - (c + x) * (n - i) + b[i] * (n - i) + x * (n - i - 1)) {
      ans = ans - (c + x) * (n - i) + b[i] * (n - i) + x * (n - i - 1);
      c = b[i];
    }
  }
  cout << ans << endl;
  return 0;
}
