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 N;
int x;
long long A[2005];
long long B[2005];
int C[2005];
void slove() {}
int main(int argc, char* argv[]) {
  cin >> N >> x;
  for (int i = 0; i < N; ++i) {
    cin >> A[i];
  }
  int s = 0;
  int mi = 0;
  int mj = 0;
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < N; ++j) {
      B[j] = A[j];
      if (j > i) {
        B[j] = B[j] + (N - j + i) * x;
        C[j] = (N - j + i);
      } else if (j < i) {
        B[j] = B[j] + (i - j) * x;
        C[j] = (i - j);
      } else {
        C[j] = 0;
      }
    }
    mi = min_element(B, B + N) - B;
    mj = max(mj, C[mi]);
    s += A[mi];
  }
  s += x * mj;
  cout << s << endl;
  return 0;
}
