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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/*AMETHYSTS*/
#pragma comment(linker, "/STACK:1000000000")
#include <cstdio>
#include <iostream>
#include <ctime>
#include <string>
#include <vector>
#include <cmath>
#include <algorithm>
#include <cstring>
#include <set>
#include <map>
#include <cstdlib>
#include <ctime>
#include <cassert>
#include <bitset>
#include <deque>
#include <stack>
#include <climits>
#include <string>
#include <queue>
#include <memory.h>
#include <unordered_map>
#include <random>
 
#define ll long long
#define ld double
#define pii pair <int, int>
#define forn(i, n) for (ll i = 0; i < (ll)n; i++)
#define mp make_pair
#define ui unsigned int
 
using namespace std;

const int maxn = 2010;
ll v[maxn];

int main() {
	int n;

	ll x;

	cin >> n >> x;

	ll sum = 0;

	for (int i = 0; i < n; i++) {
		cin >> v[i];
		sum += v[i];
	}

	sort(v, v + n);

	for (int i = n - 1; i > 0; i--) {
		if (v[0] + x < v[i]) {
			sum -= v[i];
			sum += v[0] + x;
		}
	}

	cout << sum << endl;

	return 0;
}