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
#include<bits/stdc++.h>
using namespace std;

int main()
{
	int n,x;
	cin>>n>>x;
	
	int arr[n];
	for(int i=0;i<n;i++)
	{
		cin>>arr[i];
	}
	int ans[n]={0};
	int minn=0;
	for(int i=1;i<n;i++)
	{
		if(arr[minn]>arr[i]) minn=i;
	}
	//cout<<"mkc"<<endl;
	ans[minn]=arr[minn];
	int sum=arr[minn];
	for(int i=minn+1;i<n;i++)
	{
		if(arr[i]<= x+arr[minn])
		{
			sum+=arr[i];
		}
		else
		{
			sum=sum+x+ans[minn];
		}
		//cout<<sum<<" ";
	}
	if(minn!=0)
	{
		if(arr[0]<=x+ans[minn]) sum+=arr[0];
	    else sum+=x+ans[minn];
	    //cout<<sum<<" ";
	}
	
	
	for(int i=1;i<minn;i++)
	{
		if(arr[i]<= x+arr[minn])
		{
			sum+=arr[i];
		}
		else
		{
			sum=sum+x+ans[minn];
		}
		//cout<<sum<<" ";
	}
	cout<<sum<<endl;
	return 0;
}