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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define ll long long

template <class T>
inline void read(T &x)
{
    static char c;
    x=0;
    for(c=getchar();isspace(c);c=getchar());
    static bool sign;
    sign=0;
    if (c=='-') sign=!sign,c=getchar();
    for(;isdigit(c);x=x*10+c-'0',c=getchar());
    if (sign) x=-x;
    return;
}

#ifndef DEBUG//-DDEBUG
#define SHOW(x)
#else
#define SHOW(x) cout<<#x"="<<(x)<<endl
#endif

const int MAXN=2e3+5;
ll a[MAXN<<1];
ll best[MAXN];
const ll INF=1LL<<50;
int main()
{
	int n;
	ll x;
	scanf("%d%lld",&n,&x);
	for (int i=1;i<=n;i++)
	{
		read(a[i]);
		a[i+n]=a[i];
	}
	ll ans=INF;
	memset(best,15,sizeof(best));
	for (int ev=0;ev<n;ev++)
	{
		ll sum=ev*x;
		for (int i=1;i<=n;i++)
		{
			best[i]=min(best[i],a[i+ev]);
			sum+=best[i];
		}
		ans=min(ans,sum);
	}
	printf("%lld",ans);
    return 0;
}