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>
#define ll long long
using namespace std;
const int MAXN=2010;
ll f[MAXN],a[MAXN],x;
int n;
int main()
{
	scanf("%d",&n);
	scanf("%lld",&x);
	for (int i=1;i<=n;i++) {
		scanf("%lld",&a[i]);
	}
	ll sum=1000000000000000000;
	for (int i=1;i<=n;i++) f[i]=a[i];
	for (int i=0;i<n;i++)
	{
		ll ans=(long long)i*x;
		for (int j=1;j<=n;j++)
		{
			f[j]=min(f[j],a[(i+j-1)%n+1]);
			ans+=f[j];
		}
		sum=min(sum,ans);
	}
	cout << sum << endl;
}