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 N, x;
int main() {
  cin >> N >> x;
  vector<long long> S(N);
  for (int i = 0; i < N; i++) {
    cin >> S.at(i);
  }
  long long ans[N][N];
  for (int i = 0; i < N; i++) {
    if (i == 0) {
      for (int j = 0; j < N; j++) {
        ans[i][j] = S.at(j);
      }
    } else {
      for (int j = 0; j < N; j++) {
        if (j == 0)
          ans[i][j] = min(ans[i - 1][N - 1], ans[i - 1][0]);
        else
          ans[i][j] = min(ans[i - 1][j - 1], ans[i - 1][j]);
      }
    }
  }
  for (int i = 0; i < N; i++) {
    S.at(i) = x * i;
    for (int j = 0; j < N; j++) {
      S.at(i) += ans[i][j];
    }
  }
  for (int i = 0; i < N; i++) {
    cout << S.at(i) << endl;
  }
  sort(S.begin(), S.end());
  cout << S.at(0) << endl;
}
