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

long long a[2010], c[2010], min[2010]={0}, P=0, r=0, t[2010][2010]={{0}}, x;

int llintcmp(const void *a, const void *b) {
	long long c = *(long long *)a-*(long long *)b;
	if (c>0) return 1;
	else if (c==0) return 0;
	else return -1;
}

int main() {
	int b, i, j, k, N;
	scanf("%d%lld", &N, &x);
	for (i=0;i<N;i++) scanf("%lld", &a[i]);

	c[0] = 0;
	for (i=0;i<N;i++) min[i] = a[i];
	for (i=0;i<N;i++) c[0] += a[i];
	for (k=1;k<N;k++) {
		c[k] = x*k;
		for (i=0;i<N;i++) {
			if (i>=k) b = i-k; else b = N+i-k;
			if (min[i] > a[b]) min[i] = a[b];
		}
		for (i=0;i<N;i++) c[k] += min[i];
	}
	qsort(c, N, sizeof(long long), llintcmp);

	printf("%lld\n", c[0]);
	return 0;
}