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 path(long start, long goal, long N) {
  if (goal >= start) {
    return goal - start;
  } else {
    return N - (start - goal);
  }
}
int main() {
  long N;
  long x;
  cin >> N >> x;
  vector<long> a(N);
  for (int i = 0; i < N; i++) {
    cin >> a.at(i);
  }
  long ans = 0;
  long pathtime = 0;
  for (int i = 0; i < N; i++) {
    long mintime = 10000000000;
    long pathtimej = 0;
    for (int j = 0; j < N; j++) {
      if (path(j, i, N) * x + a.at(j) < mintime) {
        mintime = path(j, i, N) * x + a.at(j);
        pathtimej = path(j, i, N);
      } else if (path(j, i, N) * x + a.at(j) == mintime) {
        pathtimej = min(pathtimej, path(j, i, N));
      }
    }
    pathtime = max(pathtime, pathtimej);
    ans += mintime - pathtimej * x;
  }
  cout << ans + pathtime * x << endl;
}
