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;
  std::cin >> n >> x;
  vector<long long> a(n, 0);
  long long mini = -1;
  long long minv = 1e10;
  long long result = 0;
  for (int i = 0; i < n; i++) {
    std::cin >> a[i];
    if (a[i] < minv) {
      mini = i;
      minv = a[i];
    }
    result += a[i];
  }
  long long rensa = 0;
  long long max_rensa = 0;
  long long now = -1;
  for (int i = mini; i < 3 * n; i++) {
    if (rensa == 0) {
      now = a[i % n];
    }
    if (a[(i + 1) % n] > now + (rensa + 1) * x) {
      rensa++;
      max_rensa = max(max_rensa, rensa);
      result -= a[(i + 1) % n];
      result += now;
      a[(i + 1) % n] = a[i % n] + x;
    } else {
      rensa = 0;
    }
  }
  std::cout << result + max_rensa * x << std::endl;
}
