/*	author:  Kite_kuma
	created: 2022.01.21 21:28:30 */

// #ifdef LOCAL
// #define _GLIBCXX_DEBUG
// #endif
#include <bits/stdc++.h>
using namespace std;

#pragma region macros

#define foa(s, v) for(auto &s : v)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define popcnt(n) __builtin_popcountll((long long)n)

#define REPname(a, b, c, d, e, ...) e
#define rep(...) REPname(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)
#define REP0(x) for(int Counter_in_rep_macro = 0; Counter_in_rep_macro < (x); ++Counter_in_rep_macro)
#define REP1(i, x) for(int i = 0; i < (x); ++i)
#define REP2(i, l, r) for(int i = (l); i < (r); ++i)
#define REP3(i, l, r, c) for(int i = (l); i < (r); i += (c))

#define DREPname(a, b, c, d, e, ...) e
#define drep(...) DREPname(__VA_ARGS__, DREP3, DREP2, DREP1)(__VA_ARGS__)
#define DREP1(i, x) for(int i = (x)-1; i >= 0; --i)
#define DREP2(i, l, r) for(int i = (r)-1; i >= (l); --i)
#define DREP3(i, l, r, c) for(int i = (r)-1; i >= (l); i -= (c))

#pragma endregion

#pragma region aliases

using ll = long long;
using ld = long double;
using ull = unsigned long long;
using vi = std::vector<int>;
using vvi = std::vector<std::vector<int>>;
using vvvi = std::vector<std::vector<std::vector<int>>>;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
using vvvll = std::vector<vvll>;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
template <class T = ll>
using V = std::vector<T>;
template <class T = ll>
using VV = V<V<T>>;
template <class T = ll>
using VVV = V<V<V<T>>>;
template <class T = ll>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T = ll>
using pqdn = std::priority_queue<T>;

#pragma endregion

#pragma region constants

const int inf = 1e9;
const long long INF = 1e18;
const long double pi = acos(-1);
const char dl = '\n';
const char sp = ' ';
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};

const int mod_1000000007 = 1000000007;
const int mod_998244353 = 998244353;

#pragma endregion

#pragma region basic_operation

template <class T0, class T1, class T2>
inline bool in_range(T0 x, T1 lef, T2 rig) {
	return ((lef <= x) && (x < rig));
}

template <class T>
inline bool chmin(T &a, T b) {
	if(a > b) {
		a = b;
		return true;
	}
	return false;
}
template <class T>
inline bool chmax(T &a, T b) {
	if(a < b) {
		a = b;
		return true;
	}
	return false;
}

void Yes(bool f = 1) { std::cout << (f ? "Yes" : "No") << '\n'; }
void No() { std::cout << "No\n"; }
void YES(bool f = 1) { std::cout << (f ? "YES" : "NO") << '\n'; }
void NO() { std::cout << "NO\n"; }

template <class T>
void drop(T answer) {
	std::cout << answer << '\n';
	exit(0);
}

void err(bool flag = true) {
	if(!flag) return;
	std::cout << -1 << '\n';
	exit(0);
}

template <class T>
void vout(std::vector<T> const &v, bool vertically = 0) {
	if(vertically) {
		for(auto const &a : v) {
			std::cout << a << '\n';
		}
		return;
	}
	for(auto it = v.begin(); it != v.end(); it++) {
		std::cout << (*it);
		if(it != v.end() - 1) {
			std::cout << ' ';
		}
	}
	std::cout << '\n';
	return;
}

inline void print() { std::cout << '\n'; }
template <class T>
inline void print(T x) {
	std::cout << x << '\n';
	return;
}
template <typename Head, typename... Tail>
void print(Head H, Tail... T) {
	std::cout << H << " ";
	print(T...);
}

template <class T>
void add(std::vector<T> &v, T val) {
	for(auto &a : v) a += val;
	return;
}

template <class T>
T dup(T a, T b) {
	assert(b != 0);
	return (a + b - 1) / b;
}

template <class T>
T greatest_lower_multiple(T x, T d) {
	if(d == 0) return 0;
	if(d < 0) d *= -1;
	T y = x % d;
	if(y < 0) y += d;
	return x - y;
}

template <class T>
T least_upper_multiple(T x, T d) {
	return -greatest_lower_multiple(-x, d);
}

long long POW(long long a, long long n) {
	long long res = 1;
	while(n > 0) {
		if(n & 1) res = res * a;
		a = a * a;
		n >>= 1;
	}
	return res;
}

long long modpow(long long a, long long n, long long mod) {	 // a^n mod
	assert(n >= 0 && mod);
	if(mod == 1) return 0LL;
	long long res = 1;
	a %= mod;
	while(n > 0) {
		if(n & 1) res = res * a % mod;
		a = a * a % mod;
		n >>= 1;
	}
	return res < 0 ? res + mod : res;
}

// return x which satisfies a * x % mod == gcd(a, mod)
// not (mod | a)
long long modinv(long long a, long long mod) {
	long long b = mod, u = 1, v = 0;
	while(b) {
		long long t = a / b;
		a -= t * b;
		std::swap(a, b);
		u -= t * v;
		std::swap(u, v);
	}
	u %= mod;
	if(u < 0) u += mod;
	return u;
}

template <class T>
int lb(const std::vector<T> &a, const T x) {
	return std::distance(a.begin(), std::lower_bound(a.begin(), a.end(), x));
}
template <class T>
int ub(const std::vector<T> &a, const T x) {
	return std::distance(a.begin(), std::upper_bound(a.begin(), a.end(), x));
}
template <class T>
void unq_sort(std::vector<T> &a) {
	std::sort(a.begin(), a.end());
	a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<int> press(std::vector<T> &a) {
	auto vec = a;
	unq_sort(vec);
	std::vector<int> ret;
	for(auto &v : a) ret.push_back(lb(vec, v));
	return ret;
}

#pragma endregion

#pragma region input
#define VEC(type, name, size) \
	vector<type> name(size);  \
	scanner::INPUT(name)
#define VVEC(type, name, h, w)                     \
	vector<vector<type>> name(h, vector<type>(w)); \
	scanner::INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LL(...)            \
	long long __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define STR(...)        \
	string __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define CHR(...)      \
	char __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define DBL(...)        \
	double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LD(...)              \
	long double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define TPL3(type0, type1, type2, name)   \
	std::tuple<type0, type1, type2> name; \
	scanner::INPUT(name);
#define TPL4(type0, type1, type2, type3, name)   \
	std::tuple<type0, type1, type2, type3> name; \
	scanner::INPUT(name);

namespace scanner {
template <class T>
void scan(T &a) {
	std::cin >> a;
}

template <class T, class L>
void scan(std::pair<T, L> &p) {
	scan(p.first);
	scan(p.second);
}

template <class T0, class T1, class T2>
void scan(std::tuple<T0, T1, T2> &p) {
	T0 t0;
	T1 t1;
	T2 t2;
	scan(t0);
	scan(t1);
	scan(t2);
	p = std::make_tuple(t0, t1, t2);
}

template <class T0, class T1, class T2, class T3>
void scan(std::tuple<T0, T1, T2, T3> &p) {
	T0 t0;
	T1 t1;
	T2 t2;
	T3 t3;
	scan(t0);
	scan(t1);
	scan(t2);
	scan(t3);
	p = std::make_tuple(t0, t1, t2, t3);
}

template <class T>
void scan(std::vector<T> &a) {
	for(auto &i : a) scan(i);
}

void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &... tail) {
	scan(head);
	INPUT(tail...);
}
}  // namespace scanner

template <typename T1, typename T2>
std::istream &operator>>(std::istream &is, std::pair<T1, T2> &p) {
	is >> p.first >> p.second;
	return is;
}
#pragma endregion

#pragma region debug

#pragma region output
template <typename T1, typename T2>
std::ostream &std::operator<<(std::ostream &os, const std::pair<T1, T2> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
std::ostream &std::operator<<(std::ostream &os, const std::vector<T> &v) {
	for(int i = 0; i < (int)v.size(); i++) {
		if(i) os << " ";
		os << v[i];
	}
	return os;
}
#pragma endregion

#pragma region view

namespace viewer {
void view(const long long e) {
	if(e == INF)
		std::cerr << "INF";
	else if(e == -INF)
		std::cerr << "-INF";
	else
		std::cerr << e;
}

void view(const int e) {
	if(e == inf)
		std::cerr << "inf";
	else if(e == -inf)
		std::cerr << "-inf";
	else
		std::cerr << e;
}

template <typename T>
void view(const T e) {
	std::cerr << e;
}

template <typename T, typename U>
void view(const std::pair<T, U> &p) {
	std::cerr << "(";
	view(p.first);
	std::cerr << ", ";
	view(p.second);
	std::cerr << ")";
}

template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ")";
}

template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ", ";
	view(std::get<3>(p));
	std::cerr << ")";
}

template <typename T>
void view(const std::set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<T> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
	std::cerr << "{\n";
	for(const auto &v : vv) {
		std::cerr << "\t";
		view(v);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
	std::cerr << "{\n";
	for(const auto &c : v) {
		std::cerr << "\t(";
		view(c.first);
		std::cerr << ", ";
		view(c.second);
		std::cerr << ")\n";
	}
	std::cerr << "}";
}

template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <typename T, typename U>
void view(const std::map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}
}  // namespace viewer

#pragma endregion

// when debugging : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	viewer::view(H);
	std::cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                                \
	do {                                                          \
		std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                                   \
		std::cerr << "\b\b]\n";                                   \
	} while(0)
#define dump(x)                                      \
	do {                                             \
		std::cerr << __LINE__ << " " << #x << " : "; \
		viewer::view(x);                             \
		std::cerr << '\n';                           \
	} while(0)

#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

#pragma endregion

#pragma region graph

template <class T = long long>
struct edge {
	T len;
	int from;
	int to;
	bool operator<(const edge a) const {
		if(len != a.len) return len < a.len;
		if(from != a.from) return from < a.from;
		return to < a.to;
	}
	bool operator>(const edge a) const {
		if(len != a.len) return len > a.len;
		if(from != a.from) return from > a.from;
		return to > a.to;
	}
};
template <class T = long long>
struct graph {	// 0-indexed
	T const INF = numeric_limits<T>::max() / 3;
	vector<vector<edge<T>>> edges;
	int ver;

	// constructor
	graph() = default;
	graph(int vertex) : ver(vertex), edges(vertex) {}

	//辺の追加 (0-indexed)
	void update(int from, int to, T len = 1, bool direction = 1) {	// checked
		edge<T> e;
		e.len = len;
		e.from = from;
		e.to = to;
		edges[from].push_back(e);
		if(!direction) {
			swap(e.to, e.from);
			edges[to].push_back(e);
		}
	}

	//入力受取 (1-indexed)
	void input(int edge_num, bool direction = false, bool weight = false, int index = 1) {	// checked
		for(int i = 0; i < edge_num; i++) {
			int a;
			int b;
			cin >> a >> b;
			a -= index;
			b -= index;
			T c;
			if(weight)
				cin >> c;
			else
				c = 1;
			update(a, b, c, direction);
		}
	}

	// 辺の長さを全て1とみたときの単一始点最短経路 (無理なときはINF)
	vector<T> bfs(int start) {	// checked
		// https://atcoder.jp/contests/abc007/submissions/me
		vector<T> ret(ver, INF);
		queue<int> q;
		q.push(start);
		ret[start] = 0;
		while(!q.empty()) {
			int now = q.front();
			q.pop();
			for(auto &e : edges[now]) {
				if(ret[e.to] != INF) continue;
				q.push(e.to);
				ret[e.to] = ret[now] + 1;
			}
		}
		return ret;
	}

	vector<T> zero_one_bfs(int start) {	 // checked
		vector<T> ret(ver, INF);
		deque<int> deq;
		deq.push_back(start);
		ret[start] = 0;
		while(!deq.empty()) {
			int now = deq.front();
			deq.pop_front();
			for(auto &e : edges[now]) {
				if(chmin(ret[e.to], ret[now] + e.len)) {
					if(e.len)
						deq.push_back(e.to);
					else
						deq.push_front(e.to);
				}
			}
		}
		return ret;
	}

	//長さが負のpathがないときの単一始点最短経路<vll> O((ver)log(ver)+(edge))
	vector<T> dijkstra(int start) {	 // checked
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_1_A/judge/4817136/C++14
		vector<T> ret(ver, (T)INF);													  //{dist,place}
		priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> p;  //{dist,place}
		p.push({0, start});
		ret[start] = 0;

		while(!p.empty()) {
			T dist = p.top().first;
			int place = p.top().second;
			p.pop();
			if(ret[place] < dist) continue;
			for(auto &next : edges[place]) {
				int nextplace = next.to;
				T dis = next.len;
				if(ret[nextplace] > dist + dis) {
					ret[nextplace] = dist + dis;
					p.push({ret[nextplace], nextplace});
				}
			}
		}
		return ret;
	}

	//単一始点最短経路 O((ver)*(edge))
	//辿り着けないとき ret[i] = INF;
	//ある頂点までのコストが無限に小さくなり得るとき→ ret[i] = -INF;
	vector<T> BellmanFord(int start) {	// checked
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_1_B/judge/4817139/C++14
		vector<T> ret(ver, INF);
		ret[start] = 0;
		for(int loop = 0; loop < ver - 1; loop++) {
			for(int v = 0; v < ver; v++) {
				if(ret[v] == INF) continue;
				for(auto &e : edges[v]) {
					ret[e.to] = min(ret[e.to], ret[v] + e.len);
				}
			}
		}

		//無限降下点の検索
		queue<int> q;
		vector<bool> chk(ver, 0);
		for(int v = 0; v < ver; v++) {
			if(ret[v] == INF) continue;
			for(auto &e : edges[v]) {
				if(ret[e.to] > ret[v] + e.len) {
					ret[e.to] = ret[v] + e.len;
					if(!chk[e.to]) {
						q.push(e.to);
						chk[e.to] = 1;
					}
				}
			}
		}
		while(!q.empty()) {
			int now = q.front();
			q.pop();
			for(auto &e : edges[now]) {
				if(!chk[e.to]) {
					chk[e.to] = 1;
					q.push(e.to);
				}
			}
		}
		for(int i = 0; i < ver; i++)
			if(chk[i]) ret[i] = -INF;

		return ret;
	}

	//閉路に含まれない頂点列挙
	//要素数がver未満なら閉路が存在、そうでなければ閉路は存在しない
	vector<int> topo_sort() {  // checked
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_4_B/judge/4817106/C++14
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_4_A/judge/4817110/C++14
		vector<int> num_input(ver);
		// 入次数
		for(int i = 0; i < ver; i++) {
			for(auto e : edges[i]) {
				num_input[e.to]++;
			}
		}
		// 入次数が0のノードをqueueで管理する
		queue<int> que;
		for(int i = 0; i < ver; i++) {
			if(num_input[i] == 0) {
				que.push(i);
			}
		}
		vector<int> ans;
		while(!que.empty()) {
			auto node = que.front();
			que.pop();
			ans.push_back(node);
			// 頂点の削除
			for(auto e : edges[node]) {
				num_input[e.to]--;
				// 行き先の入次数が0になったらqueueに追加
				if(num_input[e.to] == 0) {
					que.push(e.to);
				}
			}
		}
		return ans;
	}

	//{{端点、端点},直径の大きさ}
	pair<pair<int, int>, T> DiameterOfTree(bool weigh = true) {	 // checked
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_5_A/judge/4817099/C++14
		vector<T> vec;
		vec = weigh ? dijkstra(0) : bfs(0);
		int v1 = -1;
		T dia = -1;
		for(int i = 0; i < ver; i++)
			if((dia < vec[i])) {
				dia = vec[i];
				v1 = i;
			}

		vec = weigh ? dijkstra(v1) : bfs(v1);
		dia = -1;
		int v2 = -1;
		for(int i = 0; i < ver; i++)
			if((dia < vec[i])) {
				v2 = i;
				dia = vec[i];
			}

		pair<pair<int, int>, T> ans = {{v1, v2}, dia};
		return ans;
	}

	//無向木構造を根から葉に伸びる有向木構造に書き換える
	graph<T> RootToLeaf(int root) {	 // 0-indexed
		graph<T> ret(ver);
		vector<bool> chk(ver, 0);
		chk[root] = 1;
		function<void(int)> dfs = [&](int now) {
			for(auto &e : edges[now]) {
				if(chk[e.to] == 1) continue;
				chk[e.to] = 1;
				ret.update(now, e.to, e.len);
				dfs(e.to);
			}
		};
		dfs(root);
		return ret;
	}

	//無向木構造を葉から根に伸びる有向木構造に書き換える
	graph<T> LeafToRoot(int root) {	 // 0-indexed
		graph<T> ret(ver);
		vector<bool> chk(ver, 0);
		chk[root] = 1;
		function<void(int)> dfs = [&](int now) {
			for(auto &e : edges[now]) {
				if(chk[e.to] == 1) continue;
				chk[e.to] = 1;
				ret.update(e.to, now, e.len);
				dfs(e.to);
			}
		};
		dfs(root);
		ret.update(root, root, 0);
		return ret;
	}

	// LeafToRootのvector版.par[i]=iの親の頂点
	vector<int> par(int root) {	 // 0-indexed
		vector<int> ret(ver, -1);
		ret[root] = root;  // rootの親はroot
		function<void(int)> dfs = [&](int now) {
			for(auto &e : edges[now]) {
				if(ret[e.to] != -1) continue;
				ret[e.to] = now;
				dfs(e.to);
			}
		};
		dfs(root);
		return ret;
	}

	vector<edge<T>> ParentAndDistance(int root) {  // 0-indexed
		vector<edge<T>> ret(ver);
		for(int i = 0; i < ver; i++) ret[i].to = -1;
		ret[root].to = root;  // rootの親はroot
		ret[root].len = 0;	  // rootの親との距離は0
		function<void(int)> dfs = [&](int now) {
			for(auto &e : edges[now]) {
				if(ret[e.to].to != -1) continue;
				ret[e.to].to = now;
				ret[e.to].len = e.len;
				dfs(e.to);
			}
		};
		dfs(root);
		return ret;
	}

	//隣接sheet.主にwarshall用
	vector<vector<T>> GraphArray(void) {  // chkecked
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_1_C/judge/4817090/C++14
		vector<vector<T>> ret(ver, vector<T>(ver, INF));
		for(int from = 0; from < ver; from++) {
			for(auto &e : edges[from]) {
				ret[from][e.to] = e.len;
			}
			ret[from][from] = 0;
		}
		return ret;
	}

	graph<T> Prim(bool direction = 0, int start = 0) {	// checked
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_2_A/judge/4817129/C++14
		graph<T> ret(ver);
		priority_queue<edge<T>, vector<edge<T>>, greater<edge<T>>> p;
		for(auto &e : edges[start]) {
			p.push(e);
		}
		vector<bool> chk(ver, 0);
		chk[start] = 1;
		while(!p.empty()) {
			auto ed = p.top();
			p.pop();
			if(chk[ed.to]) continue;
			chk[ed.to] = 1;
			ret.update(ed.from, ed.to, ed.len, direction);
			for(auto &e : edges[ed.to]) {
				p.push(e);
			}
		}
		return ret;
	}

	//各頂点を根としたときの木の高さ
	vector<T> height(int start = 0) {  // checked
		// https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_5_B/judge/4817082/C++14
		vector<T> fir(ver, -1), sec(ver, -1);
		function<T(int, int)> dfs = [&](int now, int par) {
			T f = 0, s = 0;	 // startを根としたときのnowからの深さ1番目、2番目
			for(auto &e : edges[now]) {
				if(e.to == par) continue;
				s = max(s, dfs(e.to, now) + e.len);
				if(f < s) swap(f, s);
			}
			sec[now] = s;
			return fir[now] = f;
		};
		dfs(start, -1);
		function<void(int, int, T, T, T)> sol = [&](int now, int par, T parf, T pars, T parlen) {
			if(fir[now] + parlen == parf) parf = pars;
			sec[now] = max(sec[now], parf + parlen);
			if(fir[now] < sec[now]) swap(fir[now], sec[now]);
			for(auto &e : edges[now]) {
				if(e.to == par) continue;
				sol(e.to, now, fir[now], sec[now], e.len);
			}
			return;
		};
		sol(start, -1, -1, -1, -1);
		return fir;
	}

	//全方位木DP
	//マージ関数、上に送るための関数、単位元、はじめの根
	// 関数はstd::functionで渡す
	template <class U>
	vector<U> ReRootingDP(U &unit, function<U(U, U)> &merge, function<U(int, U, T)> &send, int root = 0) {
		auto tr = RootToLeaf(root);
		vector<vector<U>> v(ver);
		vector<U> ret(ver);	 //求める答

		function<U(int)> treeDP = [&](int now) {
			U res = unit;
			vector<U> vec;
			for(auto &e : tr.edges[now]) {
				U u = send(e.to, treeDP(e.to), e.len);
				v[now].push_back(u);
				res = merge(res, u);
			}
			return res;
		};
		treeDP(root);

		function<void(int, U, int, T)> rerooting = [&](int now, U ans_par, int par, T len) {
			if(now != root) ans_par = send(par, ans_par, len);
			int sz = v[now].size();
			vector<U> data_front(sz + 1), data_back(sz + 1);
			data_front[0] = data_back[sz] = unit;
			for(int i = 0; i < sz; i++) {
				data_front[i + 1] = merge(data_front[i], v[now][i]);
				data_back[sz - i - 1] = merge(v[now][sz - i - 1], data_back[sz - i]);
			}
			for(int i = 0; i < sz; i++) {
				auto nxtans = merge(ans_par, merge(data_front[i], data_back[i + 1]));
				rerooting(tr.edges[now][i].to, nxtans, now, tr.edges[now][i].len);
			}
			ret[now] = merge(ans_par, data_front[sz]);
			return;
		};
		rerooting(root, unit, root, 0);

		return ret;
	}

	// HL分解
};

// 強連結成分分解
struct SCC {
	graph<int> ng, rg;	// normal graph, reversed graph
	vector<int> compo;	// compo[i] = 新グラフでiが属する頂点集合番号
	vector<int> order;
	vector<bool> used;
	graph<int> ret;
	// g:元のグラフ, ret:強連結成分分解後のグラフ

	template <class T>
	SCC(graph<T> &g) : ng(g.ver), rg(g.ver), compo(g.ver, -1), used(g.ver, false) {
		for(int from = 0; from < g.ver; from++) {
			for(auto &e : g.edges[from]) {
				ng.update(e.from, e.to, 1, 1);
				rg.update(e.to, e.from, 1, 1);
			}
		}

		for(int i = 0; i < ng.ver; i++) dfs(i);
		reverse(order.begin(), order.end());
		int group = 0;
		for(auto i : order)
			if(compo[i] == -1) rdfs(i, group), group++;
		ret.edges.resize(group);
		for(int i = 0; i < g.ver; i++) {
			for(auto &e : g.edges[i]) {
				int s = compo[i], t = compo[e.to];
				if(s != t) ret.update(s, t, 1, 1);
			}
		}
	}

	int operator[](int k) { return compo[k]; }

	void dfs(int now) {
		if(used[now]) return;
		used[now] = true;
		for(auto &e : ng.edges[now]) dfs(e.to);
		order.push_back(now);
	}

	void rdfs(int now, int count) {
		if(compo[now] != -1) return;
		compo[now] = count;
		for(auto &e : rg.edges[now]) rdfs(e.to, count);
	}
};

#pragma endregion

// return g := gcd(a, b)
// set x and y which satisfy a*x + b*y = g
long long ext_gcd(long long a, long long b, long long &x, long long &y) {
	assert(a >= 0 && b >= 0);
	if(b == 0) {
		x = 1, y = 0;
		return a;
	}
	long long q = a / b;
	long long g = ext_gcd(b, a - q * b, x, y);
	long long z = x - q * y;
	x = y;
	y = z;
	return g;
}

// x % a == b, x % c == d
pair<long long, long long> crt(long long a, long long b, long long c, long long d) {
	long long x, y;
	long long g = ext_gcd(a, c, x, y);
	long long l = a / g * c;
	if(abs(b - d) % g != 0) return {0, 0};
	long long z = (d - b) / g % l * a % l * x % l + b;
	if(z < 0)
		z += l;
	else if(z >= l)
		z -= l;
	return {z, l};
}

int main() {
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
	std::cout << std::fixed << std::setprecision(15);
	srand((unsigned)time(NULL));

	const int p = 90007;
	debug(modpow(10, p - 1, p));

	ll q, x, y;
	cin >> q;
	cin >> q >> x >> y;

	while(1) {
		ll r = rand() % inf;
		if(r < 0 || std::numeric_limits<ll>::max() / q < r + 10) continue;
		ll rev = r * q + y;
		if(rev % 10 == 0) continue;
		string s = to_string(rev);
		reverse(all(s));
		ll n = stoll(s);
		if(rev % q == y && n % p == x) {
			drop(n);
		}
	}

	return 0;
}