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 int long long int
#define rep(a,b,c) for(int a=b;a<c;a++)
#define repm(a,b,c) for(int a=(b-1);a>=c;a--)
#define pb push_back
#define str string
#define INF 100000000000000000000;
#define sf(a) scanf("%d",&a)
using namespace std;
int replac(str s){double ans=0;rep(i,0,s.length()){ans+=(s[i]-'0')*pow(10,s.length()-i-1);}return (int)ans;}
typedef pair<int,int> pii;
vector<pii> vii;
signed main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n=0,x,a[2010];
    cin >> n >> x;
    rep(i,0,n){
        cin >> a[i];
    }
    int ans=0;
    int mi=INF;
    rep(i,0,n){
        mi=a[i];
        rep(j,0,n){
            if((j*x)>a[i])break;
                int f=(a[(i+j)%n]+x*j);
                if(a[i]>=f)mi=min(mi,f);
        }
        ans+=mi;
        //cout << mi;
    }
    cout << ans << endl;
return 0;
}
