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<iostream>
#include<vector>
#include<string>
#include<iomanip>
#include<set>

using namespace std;

int main()
{
	long long n,x;
	cin >> n >> x;
	vector<long long> a(n);
	for(int i=0;i<n;i++)
		cin >> a[i];

	vector<long long> mini(n);
	for(int i=0;i<n;i++)
		mini[i]=a[i];

	long long ans=1000000000000000;

	for(int i=0;i<n;i++)
	{
		long long tmp=x*i;
		for(int j=0;j<n;j++)
		{
			if(a[(j-i+n)%n]<mini[j])mini[j]=a[(j-i+n)%n];
			tmp+=mini[j];
		}
		if(tmp<ans)ans=tmp;
	}


	cout << ans << endl;


}