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<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
#define MAXN 2000
#define LL long long
#define INF 1000000000000000000
int n;
LL a[MAXN+5],x;
LL minn[MAXN+5];
LL ans;
int main()
{
	ans=INF;
	scanf("%d%lld",&n,&x);
	for(int i=0;i<n;i++)scanf("%lld",&a[i]);
	memset(minn,0x3f,sizeof(minn));
	for(LL st=0;st<n;st++)
	{
		LL sum=0;
		for(LL j=0;j<=n-1;j++)
		{
			minn[j]=min(minn[j],a[(j-st+n)%n]);
			sum+=minn[j];
		}
		ans=min(ans,sum+st*x);
	}
	printf("%lld",ans);
}