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;
int main() {
  long long N;
  cin >> N;
  long long x;
  cin >> x;
  vector<long long> data(N);
  vector<long long> lo(N);
  long long ans = 0;
  for (long long(i) = long long(0); (i) < long long(N); (i)++) {
    cin >> data[i];
    ans += data[i];
    lo[i] = data[i];
  }
  for (long long(i) = long long(1); (i) < long long(N); (i)++) {
    long long buf = 0;
    for (long long(j) = long long(0); (j) < long long(N); (j)++) {
      long long a = j - i;
      if (a < 0) a += N;
      lo[j] = ((lo[j]) < (lo[a]) ? (lo[j]) : (lo[a]));
      buf += lo[j];
    }
    ans = ((ans) < (buf + i * x) ? (ans) : (buf + i * x));
  }
  cout << (ans) << endl;
  return 0;
}
