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 = Integer.parseInt(sc.next());
		long x = Integer.parseInt(sc.next());
		long[] a = new long[N];
		for (int i = 0; i < N; i++) {
			a[i] = Integer.parseInt(sc.next());
		}

		long result = 0;
		int kaisuu = 0;
		for (int i = 0; i < N; i++) {
			if(a[i] <= x) result += a[i];
			else {
				int index = 0;
				long time = a[i];
				long rest = a[i];
				for(int j = i-1; rest >= x; j--) {
					if(j < 0) j = N-1;

					rest -= x;
					long temp = a[j];
					int k = 0;
					if(j < i) k += x * (i-j);
					else k += x * (N-j+i);
					temp += k;

					if(temp < time) {
						time = temp;
						index = j;
						if(k > kaisuu) {
							kaisuu = k;
						}
					}
				}
				result += a[index];
			}
			result += x * kaisuu;
		}

		System.out.println(result);
	}

}
