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 <stdio.h>
#include <stdlib.h>
#include <string.h>

int main() {
	int d, i, j, N;
	long long a[2010], P1=0, P2=0, r1=0, r2=0, t1[2010]={0}, t2[2010] = {0}, x;
	scanf("%d%lld", &N, &x);
	for (i=0;i<N;i++) scanf("%lld", &a[i]);

	for (i=0;i<N;i++) { t1[i] = a[i]; t2[i] = a[i]; }
	for (i=0;i<N;i++) {
		if (i>0 && t1[i]>t1[i-1]+x) { t1[i] = t1[i-1]; r1 = x; }
		else if (i==0 && t1[0] > t1[N-1]+x) { t1[0] = t1[N-1]; r1 = x; }
		if (i != N-1 && t2[i]>t2[i+1]+x*(N-1)) { t2[i] = t2[i+1]; r2 = x*(N-1); }
		else if (i==N-1 && t2[N-1] > t2[0]+x*(N-1)) { t2[N-1] = t2[0]; r2 = x*(N-1); }
	}
//	for (i=0;i<N;i++) printf("%lld\n", t[i]);
	for (i=0;i<N;i++) P1 += t1[i];
	P1 += r1;
	for (i=0;i<N;i++) P2 += t2[i];
	P2 += r2;

	printf("%lld\n", (P1>P2)?P2:P1);
	return 0;
}