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 sc = new Scanner(System.in);
		Integer n = sc.nextInt();
		Integer x = sc.nextInt();
		Integer[] a = new Integer[n + 1];
		Integer[][] b = new Integer[n + 1][n];
		Long result;
		Long cost = 0L;
		for (int i = 1; i <= n; i++) {
			a[i] = sc.nextInt();
			b[i][0] = a[i];
			cost += b[i][0];
		}
		result = cost;
		for (int k = 1; k < n; k++) {
			cost = (long) k * x;
			for (int i = 1; i <= n; i++) {
				if (i > k) {
					b[i][k] = Math.min(b[i][k - 1], a[i - k]);
				} else {
					b[i][k] = Math.min(b[i][k - 1], a[i - k + n]);
				}
				cost += b[i][k];
			}
			if (cost < result) {
				result = cost;
			}
		}
		System.out.println(result);
	}
}
