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 n,k;
int a[2333],b[2333];
long long ans=0x3f3f3f3f3f3f3f3fll,sum;
int main()
{
	ios_base::sync_with_stdio(false);
	cin>>n>>k;
	for(int i=1;i<=n;i++)cin>>a[i],b[i]=0x3f3f3f3f;
	for(int s=0;s<=n;s++)
	{
		sum=1ll*s*k;
		for(int i=1;i<=n;i++)
		{
			b[i]=min(b[i],a[(i-s+n-1)%n+1]);
			sum+=b[i];
		}
		ans=min(ans,sum);
	}
	cout<<ans<<endl;
	return 0;
}