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>
long long n, x;
int a[2010];
long long func(int r) {
  long long sum = 0;
  for (int i = 0; i < n; ++i) {
    int d = std::numeric_limits<int>::max();
    for (int j = 0; j <= r; ++j) {
      int m = i - j;
      if (m < 0) m += n;
      d = std::min(a[m], d);
    }
    sum += d;
  }
  return sum + x * r;
}
int main() {
  long long sum = 0;
  std::cin >> n >> x;
  for (int i = 0; i < n; ++i) {
    std::cin >> a[i];
  }
  int left = 0, right = n - 1;
  while (left + 2 < right) {
    if (func((left * 2 + right) / 3) < func((left + right * 2) / 3)) {
      right = (left + right * 2) / 3;
    } else {
      left = (left * 2 + right) / 3;
    }
  }
  std::cout << std::min(func(left), func(right)) << std::endl;
}
