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)

#include <bits/stdc++.h>

using namespace std;

using ll = long long;

#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define FORE(i, a, b) for(int i=(a);i<=(b);++i)
#define rep(i, n) for(int i=0;i<(n);++i)
#define repe(i, n) for(int i=0;i<=(n);++i)
#define ALL(v) (v).begin(),(v).end()
#define SP cout<<fixed<<setprecision(10)
typedef pair<int, int> P;
const int inf = (int) 1e9;
const int mod = (int) 1e9 + 7;

template<class T>
bool chmax(T &a, const T &b) {
	if (a < b) {
		a = b;
		return 1;
	}
	return 0;
}

template<class T>
bool chmin(T &a, const T &b) {
	if (b < a) {
		a = b;
		return 1;
	}
	return 0;
}

int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }

int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

int main(void) {
	cin.tie(0);
	ios::sync_with_stdio(false);
	
	int n;
	ll x;
	cin >> n >> x;
	ll a[n];
	rep(i, n) cin >> a[i];
	
	int min_index = 0;
	ll min_value = inf;
	rep(i, n) {
		if (a[i] < min_value) {
			min_value = a[i];
			min_index = i;
		}
	}
	
	
	bool get[n];
	get[min_index] = true;
	
	rep(i, 2 * n) {
		int index = i + min_index;
		if (get[index % n]) {
			if (a[(index + 1) % n] < a[index % n] + x) {
				get[(index + 1) % n] = true;
			} else {
				get[(index + 1) % n] = false;
				a[(index + 1) % n] = a[index % n] + x;
			}
		} else {
			if (a[(index + 1) % n] < a[index % n]) {
				get[(index + 1) % n] = true;
			} else {
				get[(index + 1) % n] = false;
				a[(index + 1) % n] = a[index % n];
			}
		}
	}
	
	ll sum = 0;
	rep(i, n) {
		sum += a[i];
	}
	
	cout << sum << endl;
	
	return 0;
}