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.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long x = sc.nextLong();
		long[] a = new long[N];
		LinkedList<Boolean> flag = new LinkedList<>();
		for (int i=0; i<N; i++) {
			a[i] = sc.nextLong();
			flag.add(false);
		}
		long res = 0;
		while (true) {
			for (int i=0; i<a.length; i++) {
				if (flag.get(i) || a[i]>=x) continue;
				res += a[i];
				flag.set(i, true);
			}
			if (satisfied(flag)) break;
			flag.offer(flag.poll());
			res += x;
		}
		System.out.println(res);
		sc.close();
	}
	
	private static boolean satisfied(List<Boolean> flag) {
		for (int i=0; i<flag.size(); i++) {
			if (!flag.get(i)) return false;
		}
		return true;
	}
}
