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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main(void)
{
	int N, x;

	scanf( "%d", &N );
	scanf( "%d", &x );

	vector<unsigned long long> table;
	table.resize( N );

	vector<bool> have;
	have.resize( N );


	for( int i = 0; i < N; i++ )
	{
		scanf( "%llu", &table[i] );
		have[i] = false;
	}

	int index = 0;
	unsigned long long cost = 0;

	while( true )
	{
		bool flag = true;
		for( int i = 0; i < N; i++ )
			if( have[i] == false )
			{
				flag = false;
				break;
			}
		if( flag ) break;

		int minPos = -1;
		unsigned long long minValue = 10000000000ULL;

		for( int i = 0; i < N; i++ )
		{
			if( have[(i - index + N) % N] == false && minValue > table[i] && table[i] < x )
			{
				minPos = i, minValue = table[i];
			}
		}
		if( minPos == -1 )
		{
			cost += x;
			index++;
		}
		else
		{
			have[(minPos - index + N) % N] = true;
			cost += table[minPos];
		}
	}

	printf( "%llu", cost );


	return 0;
}