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 <cstring>
#include <vector>
#include <queue>
#include <string>
#include <algorithm>
#include <iostream>
#include <map>
#include <set>
#include <functional>
#include <iostream>
#define INF 2000000000LL
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

int n;
ll x;
ll a[2001][2001];

int main(void){
	scanf("%d%lld",&n,&x);
	ll res=0;
	for(int i=0;i<n;i++){
		scanf("%lld",&a[i][0]);
		res+=a[i][0];
	}
	for(int i=0;i<n;i++){
		for(int j=1;j<n;j++){
			a[i][j]=a[i][0];
		}
	}
	for(int i=0;i<n;i++){
		for(ll j=1;j<n;j++){
			if(a[i][0]>a[(i-j+n)%n][0]+j*x){
				a[i][j]=min(a[i][j],a[(i-j+n)%n][0]);
			}
		}
	}
	for(int i=0;i<n;i++){
		for(int j=1;j<n;j++){
			a[i][j]=min(a[i][j],a[i][j-1]);
		}
	}
	for(int i=1;i<n;i++){
		ll sum=0;
		for(int j=0;j<n;j++){
			sum+=a[j][i];
		}
		res=min(res,(ll)sum+i*x);
	}
	printf("%lld\n",res);
	return 0;
}