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 <iostream>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <math.h>
#include <string>
#include <string.h>
#include <stack>
#include <queue>
#include <vector>
#include <utility>
#include <set>
#include <map>
#include <stdlib.h>

using namespace std;

#define ll long long
#define ld long double
#define EPS 0.0000000001
#define INF 10000000000LL
#define rep(i,n) for(i=0;i<n;i++)

typedef pair<int,int> pii;
int i,j;

int main(void) {
    int n,x;
    cin>>n>>x;
    static int dp[2005][2005]={};//trans,slime,cost
    rep(i,2005)rep(j,2005)
    dp[i][j]=0;
    ll sum[2005]={};//cost
    rep(i,n){
        cin>>dp[0][i];
        sum[0]+=dp[0][i];
    }
    for(i=1;i<n;i++){//trans
        rep(j,n)//j-slime
            dp[i][j]=min(dp[i-1][j],dp[0][(n+j-i)%n]);
        rep(j,n)
            sum[i]+=dp[i][j];
        sum[i]+=x*i;
    }
    ll ans=INF;
    rep(i,n)
        ans=min(ans,sum[i]);
    cout<<ans<<endl;
    return 0;
}