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: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int,int> pii;
#define endl '\n'
#define m_p make_pair
#define max 2010
#define oo 0x3f3f3f3f3f3f3f3f

int n;
ll x,sum;
ll a[max];
ll dp[max][max];

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    //freopen("fibsubseq.in","r",stdin);
    //freopen("fibsubseq.out","w",stdout);
	
	cin >> n >> x;
	for(int i=0;i<n;i++) cin >> a[i];
	
	for(int i=0;i<n;i++)
	{
		dp[i][0]=a[i];
		for(int k=1;k<n;k++)
		{
			int pos = i-k;
			if(pos<0) pos = n+pos;
			dp[i][k]=min(dp[i][k-1],a[pos]);
		}
	}
	sum = oo;
	for(int k=0;k<n;k++)
	{
		ll res = 0;
		for(int i=0;i<n;i++)
		{
			res+=dp[i][k];
		}
		sum=min(sum,res+k*x);
	}
	
	cout << sum << endl;
    return 0;
}