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
using System;
using System.Linq;
class Program{
	static void Main(){
		long[] s=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
		long[] a=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
		int[] h=new int[s[0]];
		long ans=0;
		for(int i=1;i<s[0];i++){
			if(a[i]>a[i-1]+s[1]*(h[i-1]+1)){
				a[i]=a[i-1];
				h[i]=h[i-1]+1;
			}
		}
		if(a[0]>a[s[0]-1]+s[1]*(h[s[0]-1]+1)){
			a[0]=a[s[0]-1];
			h[0]=h[s[0]-1]+1;
		}
		ans+=a[0];
		for(int i=1;i<s[0];i++){
			if(a[i]+s[1]*h[i]>a[i-1]+s[1]*(h[i-1]+1)){
				a[i]=a[i-1];
				h[i]=h[i-1]+1;
			}
			ans+=a[i];
		}
		Console.WriteLine("{0}",ans+h.Max()*s[1]);
	}
}