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<stdio.h>
using namespace std;
typedef long long ll;
struct node
{
	int mintime;
	int count = 0;
	int a;
}M[2010];
int main(void)
{
	int N, x,a[2010];
	cin >> N >> x;
	for (int i = 0; i < N; i++)
	{
		cin >> a[i];
		M[i].mintime = a[i];
		M[i].a = a[i];
	}
	for (int i = 0; i < N-1; i++)
	{
		int sum = (N - 1 - i)*x + a[i];
		if (sum < M[N-1].mintime)
		{
			M[N-1].mintime = sum;
			M[N-1].count = N - 1 - i;
			M[N-1].a = a[i];
		}
	}
	for (int i = 0; i < N-1; i++)
	{
		if (i == 0)
		{
			if (M[N - 1].mintime + x < M[0].mintime)
			{
				M[0].mintime = M[N - 1].mintime + x;
				M[i].count = M[N - 1].count + 1;
				M[i].a = M[N - 1].a;
			}
		}
		else
		{
			if (M[i-1].mintime + x < M[i].mintime)
			{
				M[i].mintime = M[i - 1].mintime + x;
				M[i].count = M[i - 1].count + 1;
				M[i].a = M[i - 1].a;
			}
		}
	}
	ll ans = 0,maxCount = 0;
	for (int i = 0; i < N; i++)
	{
		if (M[i].count > maxCount)
			maxCount = M[i].count;
		ans += M[i].a;
	}
	ans += maxCount*x;
	cout << ans << endl;
}