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: Time Limit Exceeded)

#pragma warning(disable:4996)

#include "bits/stdc++.h"
using namespace std;

typedef long long ll;
#define REP(i, n) for(int i = 0;i < n;i++)
#define REPR(i, n) for(int i = n;i >= 0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)

//* 便利な変数
namespace {
	int dx4[] = { 1, -1, 0, 0 };
	int dy4[] = { 0, 0, 1, -1 };

	int dx8[] = { 1, -1, 0, 0, 1, 1, -1, -1 };
	int dy8[] = { 0, 0, -1, 1, -1, 1, -1, 1 };

	int mDays[] = { 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };

	ll A, B, C, D, E, F, G, H, I, J, K, L, M,
		N, O, P, Q, R, S, T, U, V, W, X, Y, Z;

	const ll MOD_CONST = (ll)(1e9 + 7);
}
template <typename T>
vector<T> INP(ll n)
{
	vector<T> x;
	REP(i, n) {
		T tmp; cin >> tmp;
		x.push_back(tmp);
	}
	return move(x);
}
//* n文字1行の文字列を入力，一文字ごとの配列を返す
vector<char> SPRIT_STRING(ll n)
{
	string str; cin >> str;
	vector<char> cs(n);
	REP(i, n) cs[i] = str[i];
	return move(cs);
}
//* 文字列中から文字列を検索して別の文字列に置換する
void strReplace(std::string& str, const std::string& from, const std::string& to) {
	std::string::size_type pos = 0;
	while (pos = str.find(from, pos), pos != std::string::npos) {
		str.replace(pos, from.length(), to);
		pos += to.length();
	}
}
//* 素数関連関数
namespace PrimeLib {
	//* 素数判定 is_prime<unsigned>(N)
	template<typename T, std::enable_if_t<std::is_unsigned<T>::value, std::nullptr_t> = nullptr>
	bool is_prime(const T n) {
		if (n < 4) return n == 2 || n == 3;
		if (n % 2 == 0 || n % 3 == 0 || (n % 6 != 1 && n % 6 != 5)) return false;
		for (T i = 5; i * i <= n; i += 6) if (n % i == 0 || n % (i + 2) == 0) return false;
		return true;
	}
	//* 素数テーブル生成　エラトステネスの篩
	vector<ll> primeTable(ll n) {
		vector<bool> table(n - 1);
		vector<ll> ret;
		for (ll i = 0; i < n - 1; ++i) {
			if (table[i] == false) {
				ll num = i + 2;
				ret.push_back(i + 2);
				for (int j = i + num; j < n - 1; j += num)
					table[j] = true;	
			}
		}
		return ret;
	}
}
//* 組み合わせ計算
inline unsigned long long NChooseK(const unsigned long long& n, const unsigned long long& k)
{
	if (n  < k) return 0;
	if (0 == n) return 0;
	if (0 == k) return 1;
	if (n == k) return 1;
	if (1 == k) return n;
	typedef unsigned long long value_type;
	value_type* table = new value_type[static_cast<std::size_t>(n * n)];
	std::fill_n(table, n * n, 0);
	class n_choose_k_impl
	{
	public:

		n_choose_k_impl(value_type* table, const value_type& dimension)
			: table_(table),
			dimension_(dimension)
		{}

		inline value_type& lookup(const value_type& n, const value_type& k)
		{
			return table_[dimension_ * n + k];
		}

		inline value_type compute(const value_type& n, const value_type& k)
		{
			if ((0 == k) || (k == n))
				return 1;
			value_type v1 = lookup(n - 1, k - 1);
			if (0 == v1)
				v1 = lookup(n - 1, k - 1) = compute(n - 1, k - 1);
			value_type v2 = lookup(n - 1, k);
			if (0 == v2)
				v2 = lookup(n - 1, k) = compute(n - 1, k);
			return v1 + v2;
		}

		value_type* table_;
		value_type dimension_;
	};
	value_type result = n_choose_k_impl(table, n).compute(n, k);
	delete[] table;
	return result;
}
//* 座標nx, nyがWidth,Heightの領域内にあるかどうかのチェック
inline bool rangeCheck2D(int nx, int ny, int Width, int Height)
{
	return nx >= 0 and nx < Width and ny >= 0 and ny < Height;
}
//* bit全探索 
/*
	for (int i = 0; i < 1<<N; i++) {
		REP(j, N)
			if ((1 & i >> j) == 1) {;}
	}
*/
//* 値の二分探索
/*
	int lb = -1, ub = n;
	while (ub - lb > 1) {
		int mid = (lb + ub) / 2;
		if ( ) { // midが条件を満たす
			ub = mid; // 解の存在範囲は[lb, mid]
		} else {
			lb = mid; // 解の存在範囲は[mid, ub]
		}
	}
	int ans = ub;
*/
//* グラフのbfs 次のように格納
/*
struct edge { int to, cost; };
#define MAX_V 100
vector<edge> graph[MAX_V];
*/
//* 最短路
//* ベルマンフォード法　負の経路があっても動作
//* もし負の閉路があればfalseを返す
/*

*/
//* ワーシャル-フロイド法 全点対最短路　DPが基本 負の辺があってもOK(あると)
/*
const int MAX_V = 101;
const int inf = 100000000; // 問題に応じて設定
ll cost[MAX_V][MAX_V];
void warshallInit()
{
	REP(i, N) {
		REP(j, N) {
			if (i == j) cost[i][j] = 0;
			else cost[i][j] = inf;
		}
	}
}
void warshallFloyd()
{
	REP(k, N) {
		REP(i, N) {
			REP(j, N) {
				ll newCost = cost[i][k] + cost[k][j];
				if (cost[i][j] > newCost) {
					cost[i][j] = newCost;
				}
			}
		}
	}
}
int main()
{
	warshallInit();
	// input
	warshallFloyd();
	return 0;
}
*/

namespace abc080d {
	void abc080d()
	{
		cin >> N >> C;
		typedef tuple<int, int, int> Show; // channel, start, end
		vector<Show> shows(N);
		REP(i, N) {
			int s, t, c;
			shows[i] = make_tuple(c, s, t);
		}
		sort(shows.begin(), shows.end());

	}
}

namespace agc015b {
	void agc015b()
	{
		string str; cin >> str;
		ll cnt = 0;
		REP(i, str.size()) {
			if (str[i] == 'U') {
				cnt += 2 * i;
				cnt += (str.size() - (i + 1));
			}
			else {
				cnt += i;
				cnt += 2 * (str.size() - (i + 1));
			}
		}
		cout << cnt << endl;
	}
}

namespace abc088d {
	void abc088d() {
		string str; cin >> str;
		int ans = INT32_MAX;
		REP(i, str.size()) {
			if (i == str.size() - 1) continue;
			if (str[i] == str[i + 1]) continue;
			int n = i + 1;
			ans = min(max(n, (int)str.size() - n), ans);
		}
		if (ans == INT32_MAX) {
			cout << str.size() << endl;
		}
		else
			cout << ans << endl;
	}
}

/*
namespace arc063b {
	void arc063b()
	{
		scanf("%d %d %d", &N, &K, &L);
		static vector<int> pqs[200005];
		int p, q, r, s;

		// リンクをソートしてDFS
		
		REP(i, K) {
			scanf("%d %d", &p, &q); p--; q--;
			pqs[q].push_back(p);
			pqs[p].push_back(q);
		}
		static vector<int> link[200005];
		int link_num = 0;
		REP(i, L) {
			scanf("%d %d", &r, &s); r--; s--;
			link[r].push_back(s);
			link[s].push_back(r);
		}

		static bool visited[200005];
		static int linked1[200005], linked2[200005];
		queue<int> rest;
		REP(i, N) {
			if (visited[i]) continue;
			linked1[i] = i + 1;
			rest.push(i);
			while (not rest.empty()) {
				int current = rest.front(); rest.pop();
				for (int next : pqs[current]) {
					if (visited[next]) continue;
					rest.push(next);
					linked1[next] = i + 1;
				}
				visited[current] = true;
			}
		}
		memset(&visited[0], 0, sizeof(visited));
		REP(i, N) {
			if (visited[i]) continue;
			linked2[i] = i + 1;
			rest.push(i);
			while (not rest.empty()) {
				int current = rest.front(); rest.pop();
				for (int next : link[current]) {
					if (visited[next]) continue;
					rest.push(next);
					linked2[next] = i + 1;
				}
				visited[current] = true;
			}
		}

		map<pair<int, int>, int> cnt;
		memset(&visited[0], 0, sizeof(visited));
		REP(i, N) REP(j, N) 
			if (not visited[i] and not visited[j] and linked1[i] == linked1[j] and linked2[i] == linked2[j]) {
				visited[i] = true;
				visited[j] = true;
				cnt[make_pair(linked1[i], linked2[i])]++;
			}
		
		REP(i, N) {
			cout << cnt[make_pair(linked1[i], linked2[i])];
			if (i != N - 1) cout << " ";
			else cout << endl;
		}
	}
}*/

namespace abc075d {
	void abc075d()
	{
		cin >> N >> K;
		vector<pair<int, int>> pos(N);
		REP(i, N) cin >> pos[i].first >> pos[i].second;
		
		ll ans = INT64_MAX;
		REP(i, N) {
			REP(j, N) {
				pair<int, int> p1 = pos[i], p2 = pos[j];
				int cnt = 0;
				REP(k, N) {
					int x = pos[k].first, y = pos[k].second;
					if (k == i or k == j)
						cnt++;
					else {
						bool ox = false, oy = false;
						if (p1.first <= p2.first) {
							if (p1.first <= x and
								x <= p2.first)
								ox = true;
						}
						else {
							if (p2.first <= x and
								x <= p1.first)
								ox = true;
						}
						if (p1.second <= p2.second) {
							if (p1.second <= y and
								y <= p2.second)
								oy = true;
						}
						else {
							if (p2.second <= y and
								y <= p1.second)
								oy = true;
						}
						if (ox and oy) cnt++;
					}
				}
				if (cnt >= K)
					ans = min(ans, (ll)(abs(p1.first - p2.first) * abs(p1.second - p2.second)));
			}
		}
		cout << ans << endl;
	}
}

namespace abc088c {
	struct edge {
		int from, to, cost;
	};
	bool bellmanFord(vector<edge>& es, vector<ll>& ds, int start) {
		for (auto& d : ds) d = INT64_MAX;
		ds[start] = 0;
		for (int n = 0; n < ds.size(); ++n) {
			for (int i = 0; i < es.size(); ++i) {
				edge e = es[i];
				if (ds[e.from] != INT64_MAX and
					ds[e.to] > ds[e.from] + e.cost) {
					ds[e.to] = ds[e.from] + e.cost;
					if (n == ds.size() - 1)
						return false;
				}
			}
		}
		return true;
	}
	void abc088c()
	{
		cin >> H >> W;
		vector<string> field(H);
		vector<edge> es;
		REP(i, H) cin >> field[i];
		REP(i, H) {
			REP(j, W) {
				if (j + 1 < W and 
					field[i][j] == '.' and
					field[i][j + 1] == '.') {
					int p1 = i * W + j, p2 = p1 + 1;
					es.push_back(edge{ p1, p2, 1 });
					es.push_back(edge{ p2, p1, 1 });
				}
				if (i + 1 < H and
					field[i][j] == '.' and
					field[i + 1][j] == '.') {
					int p1 = i * W + j, p2 = p1 + W;
					es.push_back(edge{ p1, p2, 1 });
					es.push_back(edge{ p2, p1, 1 });
				}
			}
		}
		vector<ll> ds(H*W);
		bellmanFord(es, ds, 0);
		int cnt = 0;
		REP(i, H) {
			REP(j, W) {
				if (field[i][j] == '.') cnt++;
			}
		}
		if (ds[ds.size() - 1] == INT64_MAX)
			cout << "-1" << endl;
		else
			cout << cnt - 1 - ds[ds.size() - 1] << endl;
	}
}

namespace arc093d {
	void arc093d() {
		cin >> N;
		vector<ll> as(N);
		ll sum = 0;
		ll pos = 0;
		REP(i, N) {
			cin >> as[i];
			sum += abs(pos - as[i]);
			pos = as[i];
		}
		sum += abs(pos);

		REP(i, N) {
			ll before = (i == 0) ? 0 : as[i - 1];
			ll after = (i == N - 1) ? 0 : as[i + 1];
			cout << sum - abs(before - as[i]) + abs(before - after) - abs(after - as[i]) << endl;
		}
	}
}

namespace agc004b {
	void agc004b() {
		cin >> N >> X;
		vector<int> as(N);
		REP(i, N) cin >> as[i];

		ll ans = 999999999999999;
		REP(k, N) {
			ll lans = k * X;
			REP(i, N) {
				int bik = as[i];
				FOR(j, 1, k+1) {
					int idx = (i >= j) ? i - j : N - (j - i);
					bik = min(bik, as[idx]);
				}
				lans += bik;
			}
			ans = min(ans, lans);
		}
		cout << ans << endl;
	}
}

int main()
{
	cin.tie(0);
	ios::sync_with_stdio(false);
	//arc084b::arc084b();
	//arc093c::arc093c();
	agc004b::agc004b();
	return 0;
}