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;
int x;
int a[2000];
int main() {
  scanf("%d %d", &n, &x);
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < n; i++) {
    int min = INT_MAX;
    int mini = 0;
    for (int j = 0; j < n; j++)
      if (min > a[j]) {
        min = a[j];
        mini = j;
      }
    for (int j = mini + 1; j < mini + n / 2 + 1; j++) {
      if (a[j % n] > a[mini] + x * (j - mini))
        a[j % n] = a[mini] + x * (j - mini);
    }
    for (int j = mini - 1; j > mini - n / 2 - 1; j--) {
      if (a[j >= 0 ? j : n + j] > a[mini] + x * (mini - j))
        a[j >= 0 ? j : n + j] = a[mini] + x * (mini - j);
    }
  }
  int ans = 0;
  for (int i = 0; i < n; i++) ans += a[i];
  printf("%d\n", ans);
}
