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() {
  int N, x;
  vector<long long> A;
  vector<bool> colors;
  vector<bool> colors_temp;
  cin >> N;
  cin >> x;
  A.resize(N);
  colors.resize(N);
  colors_temp.resize(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    colors[i] = false;
    colors_temp[i] = false;
  }
  long long sum = 0;
  int num_true = 0;
  while (num_true < N) {
    for (int i = 0; i < N; i++) {
      if (colors[i] == false && A[i] <= x) {
        sum += A[i];
        colors[i] = true;
        num_true++;
      }
    }
    if (num_true < N) {
      sum += x;
      for (int i = 0; i < N; i++) {
        colors_temp[(i + 1) % N] = colors[i];
      }
      for (int i = 0; i < N; i++) {
        colors[i] = colors_temp[i];
      }
    }
  }
  cout << sum << endl;
  return 0;
}
