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){
		Scanner scan = new Scanner(System.in);
		double N = scan.nextDouble();
		double x = scan.nextDouble();
		double a[] = new double[(int)N];
		for(int i=0;i<N;i++){
			a[i] = scan.nextDouble();
		}
		double aa[] = new double[(int)N];
		for(int i=0;i<N;i++){
			if(i==0){
				aa[i] = Math.min(a[i], a[(int)N-1]+x);
			}else{
				aa[i] = Math.min(a[i], aa[i-1]+x);
			}
		}
		int count = 0;
		for(int i=0;i<N;i++){
			if(i==0){
				aa[i] = Math.min(aa[i], aa[(int)N-1]+x);
				if(aa[i]==a[(int)N-1]+x){
					count++;
				}
			}else{
				aa[i] = Math.min(aa[i], aa[i-1]+x);
				if(aa[i]==a[i-1]+x){
					count++;
					if(i-1==0){
						count--;
					}
				}
			}
		}
		int output = 0;
		for(int i=0;i<N;i++){
			output += (int)aa[i];
			//System.out.println((int)aa[i]);
		}
		System.out.println((int)(output-count*x));

	}
}