Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
#include <cstring>
#include <map>
#include <queue>
#include <string>
#define pb push_back
#define mod 1000000007
#define all(x) x.begin(),x.end()
#define inf (int)(1e9)
using namespace std;
typedef long long int ll;
typedef pair<int,int> pii;

ll a[2222];
ll b[2222];
int main(void){
  ll n,x;
  cin>>n>>x;
  cin>>a[1];
  b[1]=a[1];
  int t,tm;
  tm=a[1];
  for(int i=2;i<=n;i++){
    cin>>a[i];
    b[i]=min(a[i],b[i-1]+x);
    if(tm>b[i]){tm=b[i];t=i;}
  }
  b[1]=min(b[1],b[n]+x);
  if(tm>b[1]){tm=b[1];t=1;}
  /*
  ll res=tm;
  for(int i=t+1;i<=n;i++){
    if(a[i]>b[i]) res+=tm+x;
    else res+=a[i];
  }
  for(int i=1;i<t;i++){
    if(a[i]>b[i]) res+=tm+x;
    else res+=a[i];
  }
  */
  ll res=0;
  for(int i=1;i<=n;i++){
    if(a[i]>b[i]) res+=tm + x;
    else res+=a[i];
  }
  cout<<res<<endl;

  return 0;
}