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>
using namespace std;
int main(){
  long long n,x,ans=0,cnt,MAXcnt=0,cmp;
  cin >> n >> x;
  long long a[n],tmp[n]={},cntt[n]={};
  bool f=true;
  for(int i=0;i<n;i++){
    cin >> a[i];
  }
  for(int i=n-1;i>=0;i--){
    if(a[i]<=x){
      tmp[i]=a[i];
      cntt[i]=0;
    }else{
      tmp[i]=a[i];
      cnt=0;
      for(int j=i-1;j>=0;j--){
        cnt++;
        if(tmp[i]>a[j]+cnt*x){
          tmp[i]=a[j]+cnt*x;
          cmp=cnt;
        }
      }
      for(int j=n-1;j>i;j--){
        cnt++;
        if(tmp[i]>a[j]+cnt*x){
          tmp[i]=a[j]+cnt*x;
          cmp=cnt;
        }
      }
      MAXcnt=max(MAXcnt,cmp);
      cntt[i]=cmp;
    }
  }
  for(int i=0;i<n;i++){
    if(cntt[i]==MAXcnt and f){
      ans+=tmp[i];
      f=false;
    }else{
      ans+=tmp[i]-cntt[i]*x;
    }
  }
  cout << ans << endl;
  return 0;
}