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,n) for(int (i)=0;(i)<(n);(i)++)
// const bool debug=true;
const bool debug=false;
#define DEBUG if(debug==true)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const ll MOD = 1000000007;

int main(void) {
    ll n,x;
    cin>>n>>x;
    ll a[n];
    ll time[n];
    ll lim = 1LL<<60;
    ll dif[n]={};
    ll from[n]={};
    rep(i,n){cin>>a[i];}
    rep(i,n){time[i]=a[i];}
    rep(i,n){from[i]=a[i];}
    rep(i,n){
        rep(j,n){
            if(time[(i+j)%n]>a[i]+x*j){
                time[(i+j)%n] = a[i]+x*j;
                dif[(i+j)%n] = x*j;
                from[(i+j)%n] = a[i];
            }
        }
    }
    ll res=0;
    rep(i,n){
        res = max(res, dif[i]);        
    }
    rep(i,n){
        res += from[i];
    }
    cout << res << endl;
    return 0;
}
