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);
		int n = sc.nextInt();
		long x = sc.nextLong();
		int[] a = new int[n];
		int[] b = new int[n];

		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}

		b = a.clone();

		long ans = Long.MAX_VALUE;

		for (int k = 0; k < n; k++) {

			long xk = x * k;
			long sum = 0;

			for (int i = 0; i < n; i++) {
				b[i] = Math.min(b[i], a[(i - k + n) % n]);
				sum += b[i];
			}

			ans = Math.min(ans, sum + xk);

		}

		System.out.println(ans);

	}

}
