Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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]);
	}
}