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 <iostream>
#include <set>
#include <map>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
#include <cstdio>
#include <climits>
#include <ctime>
#include <cassert>
#include <queue>
#include <deque>
#include <stack>
#include <memory.h>
#include <bitset>
#include <cstring>
#include <assert.h>
#include <random>

using namespace std;

#pragma comment(linker, "/STACK:64000000")

#define ll long long
#define mp make_pair

const double pi = 3.14159265358979323846;
const double eps = 1e-6;
const ll maxn = 2001;
const ll inf = 1000000007;
const ll mod = 1000000007;

ll n, a[maxn], sum, x, k[maxn], su[maxn], d[maxn];
set<pair<ll, ll> > s;

ll dst(ll y, ll z) {
	if (z > y)
		return z - y;
	else
		return z + n - y;
}

void solve() {
	while (!s.empty()) {
		ll ver = s.begin()->second;
		ll val = s.begin()->first;
		s.erase(s.begin());
		if (val != d[ver])
			continue;
		for (int i = 0; i < n; i++) {
			if (i == ver)
				continue;
			if (d[i] > d[ver] + x * dst(ver, i)) {
				d[i] = d[ver] + x * dst(ver, i);
				k[i] = dst(ver, i) + k[ver];
				su[i] = su[ver];
				s.insert(mp(su[i], i));
			}
		}
	}
}

int main() {
	
	cin >> n >> x;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		d[i] = a[i];
		su[i] = a[i];
		k[i] = 0;
		s.insert(mp(a[i], i));
	}
	solve();
	ll ms = 0;
	for (int i = 0; i < n; i++) {
		ms = max(ms, k[i]);
		sum += su[i];
	}
	cout << sum + x * ms;
	return 0;
}