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 <stdio.h>
#define N 2005
typedef long long ll;
int n,x,d[N*2],f[N][N];
inline int min(int a,int b){return a<b?a:b;}
int main() {
	scanf("%d%d",&n,&x);
	int* const a=d+n;
	for(int i=0;i<n;++i) scanf("%d",d+i),a[i]=d[i];
	for(int i=0;i<n;++i) {
		f[i][0]=a[i];
		for(int j=1;j<n;++j) f[i][j]=min(f[i][j-1],a[i-j]);
	}
	ll ans=1LL<<60,tmp;
	for(int j=0;j<n;++j) {
		tmp=(ll)j*x;
		for(int i=0;i<n;++i) tmp+=f[i][j];
		if(tmp<ans) ans=tmp;
	}
	printf("%lld",ans);
	return 0;
}