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++ (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
long long a[40010];
long long q[40010];
int l,r;
int main()
{
	int n;
	long long x;
	cin>>n>>x;
	for(int i=1;i<=n;i++)
	  {
	  	scanf("%lld",&a[i]);
	  }
	for(int i=n+1;i<=n+n;i++)
	  a[i]=a[i-n];
	long long lastans=0;
	for(int xx=0;xx<=n;xx++)
	  {
	  	l=1;
	  	r=0;
	  	long long ans=0;
	  	for(int i=n+1-xx;i<=n;i++)
	  	  {
	  	  	while(r>=l&&a[i]<q[r])
	  	  	  r--;
	  	  	q[++r]=i;
		  }
		for(int i=n+1;i<=n+n;i++)
		  {
		  	while(l<=r&&q[l]<i-xx)
		  	  l++;
		  	while(r>=l&&a[i]<a[q[r]])
	  	  	  r--;
	  	  	q[++r]=i;
	  	  	ans+=a[q[l]];
		  }
		if(lastans==0||lastans>ans+(long long)xx*x)
		  lastans=ans+(long long)xx*x;
	  }
	cout<<lastans;
}