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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class AGC004B{

	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner(System.in);
		int n;
		long x;
		n = sc.nextInt();
		x = sc.nextLong();
		long[] a = new long[n];
		for(int i=0; i<n; i++) a[i] = sc.nextLong();
		long[] b = a.clone();
		long ans=Long.MAX_VALUE;
		for(int k=0; k<n; k++) {
			long acc=0;
			long xk = ((long)x)*k;
			for(int i=0; i<n; i++) {
				b[i]=Math.min(b[i], a[(i-k+n)%n]);
				acc+=b[i];
			}
			ans=Math.min(ans, acc+xk);
		}
		System.out.println(ans);
	}

	static class MyScanner
	{
		BufferedReader br;
		StringTokenizer st;
		public MyScanner(InputStream s) 
		{
			br=new BufferedReader(new InputStreamReader(s));
		}
		public String nextLine() throws IOException
		{
			return br.readLine();
		}
		public String next() throws IOException
		{
			while(st==null || !st.hasMoreTokens())
				st=new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
			
		}
		public double nextDouble() throws IOException
		{
			return Double.parseDouble(next());
		}
		public boolean ready() throws IOException
		{
			return br.ready();
		}
		public long nextLong() throws IOException
		{
			return Long.parseLong(next());
		}
	}
}
