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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        long x = Integer.parseInt(sc.next());
        int[] a = new int[N];
        PriorityQueue<Integer> q = new PriorityQueue<Integer>((o1, o2)->Integer.compare(o2, o1));
        int a_min = 1_500_000_000;
        long sum = 0L;
        for (int i=0;i<N;i++) {
            a[i] = Integer.parseInt(sc.next());
            sum=sum+a[i];
            q.add(a[i]);
            a_min = Math.min(a_min, a[i]);
        }

        long ans = 1_000_000_000_000_000_000L;
        for (int i=0;i<N;i++) {
            ans = Math.min(ans, sum+x*i);
            int tmp = q.remove();
            sum=sum-tmp;
            sum=sum+a_min;
        }
        System.out.println(ans);
    }
}