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<cstring>
#include<algorithm>
#define MAXN 2000
#define INF 1000000000000000000LL
using namespace std;
typedef long long LL;
int N;
LL b[MAXN+5],a[MAXN+5],x;
int main()
{
	scanf("%d %lld",&N,&x);
	for(int i=0;i<N;i++)
		scanf("%lld",&a[i]);
	fill(b,b+N,INF);
	LL ans=INF;
	for(int mv=0;mv<N;mv++)
	{
		LL ansn=0;
		for(int i=0;i<N;i++)
			b[i]=min(b[i],a[(i-mv+N)%N]);
		for(int i=0;i<N;i++)
			ansn+=b[i];
		ansn+=mv*x;
		ans=min(ans,ansn);
	}
	printf("%lld\n",ans);
	return 0;
}