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 <time.h>
#include <string.h>
#include <math.h>

#define MOD 1000000007
#define REP(i,n) for ((i)=0;i<(n);i++)
#define SET(a,c) memset(a,c,sizeof a)
#define CLR(a) memset(a,0,sizeof a)
#define MIN(a,b) (a>b?b:a)
#define MAX(a,b) (a>b?a:b)
#define LL long long
#define ULL unsigned long long

int compare_ll(const void *a, const void *b){
	return *(ULL*)b - *(ULL*)a;
}



int main(void) {
	ULL a[2000] = {0};
	int N,i, cnt, cntmax;
	ULL x;
	int flag;
	ULL ans = 0;

	scanf("%lld %lld", &N, &x);

	REP(i,N)	scanf("%lld", &a[i]);

	flag = 1;
	cntmax = 0;
	cnt = 0;

	while(flag == 1){
		flag = 0;
		for(i=1;i<N;i++){
			if(a[i] > a[i-1]+(x*(cnt+1))){
				a[i] = a[i-1];
				flag = 1;
				cnt++;
			}else{
				if(cntmax < cnt){
					cntmax = cnt;
				}
				cnt = 0;
			}
		}
		if(a[0] > a[N-1]+(x*(cnt+1))){
			a[0] = a[N-1];
			flag = 1;
			cnt++;
		}
	}

	REP(i,N) ans += a[i];
	ans += cntmax * x;

	printf("%lld", ans);

	return 0;
}

/* 最後の改行忘れるな！！ */