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;
#define ll long long

ll a[2005],b[2005][2005],n,x,ans=9e18;
int main()
{
	scanf("%lld%lld",&n,&x);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
	}
	for(int i=1;i<=n;i++)
	{
		b[i][i]=a[i];
		for(int j=i+1;j<=n;j++)
		{
			b[i][j]=min(b[i][j-1],a[j]);
		}
	}
	for(ll i=0;i<n;i++)
	{
		ll temp=i*x;
		for(ll j=1;j<=n;j++)
		{
			int k=j-i;
			if(k<=0)temp+=min(b[k+n][n],b[1][j]);
			else temp+=b[k][j];
		}
		ans=min(ans,temp);
	}
	printf("%lld",ans);
	return 0;
}