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 <iostream>
using namespace std;
typedef long long  LL;
const int N = int(2e3) + 10;
LL a[N],b[N];
LL n,x;
int f(int i){
    if(i<=0) i+=n;
    return i;
}
int main(){
    scanf("%lld %lld",&n,&x);
    LL sum=0;
    for(int i=1;i<=n;i++) {cin>>a[i];sum+=a[i];b[i]=a[i];}
    for(int i=1;i<=n-1;i++){
        LL tmp=x*i;
        for(int j=1;j<=n;j++){
            b[j]=min(b[j],a[f(j-i)]);
            tmp+=b[j];
        }
        sum=min(sum,tmp);
    }
    cout<<sum<<endl;
}
