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>
int n, x;
int a[2010], p[2010];
long long c[2010];
int main() {
  long long sum = 0;
  std::cin >> n >> x;
  for (int i = 0; i < n; ++i) p[i] = i;
  int midx = 0;
  for (int i = 0; i < n; ++i) {
    std::cin >> a[i];
    c[i] = a[i];
    if (a[midx] > a[i]) {
      midx = i;
    }
  }
  int move = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 1; j < n; ++j) {
      int m = i - j;
      if (m < 0) m += n;
      if (j * x + a[m] < c[i]) {
        p[i] = m;
        c[i] = j * x + a[m];
        move = std::max(j, move);
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    sum += a[p[i]];
  }
  sum += move * x;
  std::cout << sum << std::endl;
}
