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 rep(i,k,n) for(int i=k;i<=n;i++)
using namespace std;
const int N=2017;
typedef long long ll;
ll ans=0x3f3f3f3f3f3f3f3full;
int n,a[N],x,mi[N][N];
void solve(int k){
	ll res=1ll*k*x;
	rep(i,1,n)res+=mi[i][k];
	ans=min(ans,res);
}
int main(){
	scanf("%d%d",&n,&x);
	rep(i,1,n)scanf("%d",&a[i]);
	rep(i,1,n){
		mi[i][0]=a[i];
		
		rep(j,1,n-1)mi[i][j]=min(mi[i][j-1],a[(i-j+n-1)%n+1]);
	}
	rep(i,0,n-1)solve(i);
	printf("%lld\n",ans);
}