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<stdio.h>

#pragma GCC optimize ("Ofast")

#define stmin(a,b) ((a)<(b)?(a):(b))
typedef unsigned long long ull;
int main(void){
	int n;
	long long x;
	int i;
	scanf("%d %lld",&n,&x);
	long ar[n<<1];
	for(i = 0;i < n;i++)scanf("%ld",&ar[i]);
	for(i = 0;i < n;i++)ar[i+n] = ar[i];
	long timmin[n];
	for(i = 0;i < n;i++)timmin[i] = ar[i];
	ull minans = 1llu<<63;
	ull tmp = 0;
	for(int emc = 0;emc < n;emc++){
		tmp = 0;
		for(i = 0;i < n;i++)tmp += (timmin[i] = stmin(timmin[i],ar[i+emc]));
		minans = stmin(minans,emc*x + tmp);
	}
	printf("%llu",minans);
	return 0;
}