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
import java.util.*;

class Main {
        public static void main(String args[]) {
                Scanner sc = new Scanner(System.in);
                int N = sc.nextInt(), x = sc.nextInt();
                int[] a = new int[N];
                for (int i = 0; i < N ; i++) {
                        a[i] = sc.nextInt();
                }
                int ans = 1 << 20;
                int xmax = 0;
                for (int i = 0; i < N; i++) {
                        int memo = i * x;
                        for (int j = 0; j < N; j++) {
                                int tmp = 1 << 20;
                                for (int k = 0; k <= i; k++) {
                                        tmp = Math.min(tmp, a[(k - j + N) % N]);
                                }
                                memo += tmp;
                        }
                        ans = Math.min(ans, memo);
                }
                System.out.println(ans);
        }
}