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, x;
  cin >> N >> x;
  vector<long long> a(N);
  for (int(i) = 0; (i) < (int)(N); (i)++) cin >> a[i];
  long long ans = 0;
  long long cnt = 0, maxr = 0;
  for (int(i) = 0; (i) < (int)(N); (i)++) {
    long long mini = 1e15;
    long long cnt_diff = 0;
    for (int(j) = 0; (j) < (int)(N); (j)++) {
      long long diff = (i + N - j - 1) % N;
      if (mini > diff * x + a[(i + N - diff) % N]) {
        mini = min(mini, diff * x + a[(i + N - diff) % N]);
        maxr = max(maxr, diff);
        cnt_diff = diff;
      }
    }
    cnt += cnt_diff;
    ans += mini;
  }
  cout << ans - max((long long)0, (cnt - maxr) * x) << endl;
  return 0;
}
