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.Scanner;


public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scanner = new Scanner(System.in);
		int N = scanner.nextInt();
		int x = scanner.nextInt();
		int [] t = new int[N];
		int max = 0;
		for(int i = 0; i < N; ++i)
		{
			t[i] = scanner.nextInt();
			if(t[i] > max)
			{
				max = t[i];
			}
		}
		int min = min(t);
		if(N >= 2 && N <= 2000
				&& min >= 1 && max <= 10E9
				&& x >= 1 && x <= 10E9)
		{
			int total = 0;
			if(x > max)
			{
				for(int n : t)
				{
					if(x + min > n)
					{
						total += n;
					}
					else
					{
						total += x + min;
						if(n == t[t.length - 1])
						{
							total -= x;
						}
					}
				}
			}
			System.out.println(total);
		}
	}

	public static int min(int [] num)
	{
		int min = num[0];
		for(int n : num)
		{
			if(n < min)
			{
				min = n;
			}
		}
		return min;
	}
}
