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>

long long int N, x, a[2123], which[2123] = { -1 }, how[2123] = { -1 }, cou = 0, ans = 0;

int main() {

	scanf("%lld%lld", &N, &x);
	for (int i = 0; i < N; i++) { scanf("%lld", &a[i]); }

	for (int i = 0; i < N; i++) {
		if (a[i] > x) { which[i] = 1; }
		if (a[i] <= x) { which[i] = 0; }
	}
	for (int i = 0; i < N; i++) {
		if (which[i] == 0) {
			for (int j = i + 1; j < N; j++) {
				if (which[j] == 0) { break; }
				else { cou++; }
				if (j == N - 1) { j = -1; }
			}
			how[i] = cou;
			cou = 0;
		}
	}
	for (int i = 0; i < N; i++) {
		if (how[i] != -1) {
			ans += x*how[i];
			ans += a[i] * how[i];
		}
	}
	for (int i = 0; i < N; i++) {
		if (a[i] <= x) { ans += a[i]; }
	}

	printf("%lld", ans);

	return 0;
}