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 main() {
  int N, x, a[2001], s, big, small, width;
  long total = 0, min, temp;
  scanf("%d %d", &N, &x);
  for (int i = 1; i <= N; i++) {
    scanf("%d", &a[i]);
  }
  for (int i = 1; i <= N; i++) {
    min = a[i];
    for (int j = 1; j <= N; j++) {
      if (i == j) continue;
      if (i < j) {
        big = j;
        small = i;
      } else {
        big = i;
        small = j;
      }
      if (big - small > N / 2)
        width = N - big + small;
      else
        width = big - small;
      temp = a[j] + width * x;
      min = (min < temp) ? min : temp;
    }
    total += min;
  }
  printf("%ld\n", total);
}
