/* author: Kite_kuma created: 2022.01.21 21:28:30 */ // #ifdef LOCAL // #define _GLIBCXX_DEBUG // #endif #include 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; using vvi = std::vector>; using vvvi = std::vector>>; using vll = std::vector; using vvll = std::vector; using vvvll = std::vector; using pii = std::pair; using pll = std::pair; template using V = std::vector; template using VV = V>; template using VVV = V>>; template using pqup = std::priority_queue, std::greater>; template using pqdn = std::priority_queue; #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 inline bool in_range(T0 x, T1 lef, T2 rig) { return ((lef <= x) && (x < rig)); } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } template 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 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 void vout(std::vector 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 inline void print(T x) { std::cout << x << '\n'; return; } template void print(Head H, Tail... T) { std::cout << H << " "; print(T...); } template void add(std::vector &v, T val) { for(auto &a : v) a += val; return; } template T dup(T a, T b) { assert(b != 0); return (a + b - 1) / b; } template 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 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 int lb(const std::vector &a, const T x) { return std::distance(a.begin(), std::lower_bound(a.begin(), a.end(), x)); } template int ub(const std::vector &a, const T x) { return std::distance(a.begin(), std::upper_bound(a.begin(), a.end(), x)); } template void unq_sort(std::vector &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template std::vector press(std::vector &a) { auto vec = a; unq_sort(vec); std::vector ret; for(auto &v : a) ret.push_back(lb(vec, v)); return ret; } #pragma endregion #pragma region input #define VEC(type, name, size) \ vector name(size); \ scanner::INPUT(name) #define VVEC(type, name, h, w) \ vector> name(h, vector(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 name; \ scanner::INPUT(name); #define TPL4(type0, type1, type2, type3, name) \ std::tuple name; \ scanner::INPUT(name); namespace scanner { template void scan(T &a) { std::cin >> a; } template void scan(std::pair &p) { scan(p.first); scan(p.second); } template void scan(std::tuple &p) { T0 t0; T1 t1; T2 t2; scan(t0); scan(t1); scan(t2); p = std::make_tuple(t0, t1, t2); } template void scan(std::tuple &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 void scan(std::vector &a) { for(auto &i : a) scan(i); } void INPUT() {} template void INPUT(Head &head, Tail &... tail) { scan(head); INPUT(tail...); } } // namespace scanner template std::istream &operator>>(std::istream &is, std::pair &p) { is >> p.first >> p.second; return is; } #pragma endregion #pragma region debug #pragma region output template std::ostream &std::operator<<(std::ostream &os, const std::pair &p) { os << p.first << " " << p.second; return os; } template std::ostream &std::operator<<(std::ostream &os, const std::vector &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 void view(const T e) { std::cerr << e; } template void view(const std::pair &p) { std::cerr << "("; view(p.first); std::cerr << ", "; view(p.second); std::cerr << ")"; } template void view(const std::tuple &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 void view(const std::tuple &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 void view(const std::set &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::unordered_set &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::vector &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const std::vector> &vv) { std::cerr << "{\n"; for(const auto &v : vv) { std::cerr << "\t"; view(v); std::cerr << '\n'; } std::cerr << "}"; } template void view(const std::vector> &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 void view(const std::vector> &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 void view(const std::vector> &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 void view(const std::map &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 void view(const std::unordered_map &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 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 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 struct graph { // 0-indexed T const INF = numeric_limits::max() / 3; vector>> 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 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 bfs(int start) { // checked // https://atcoder.jp/contests/abc007/submissions/me vector ret(ver, INF); queue 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 zero_one_bfs(int start) { // checked vector ret(ver, INF); deque 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 O((ver)log(ver)+(edge)) vector dijkstra(int start) { // checked // https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_1_A/judge/4817136/C++14 vector ret(ver, (T)INF); //{dist,place} priority_queue, vector>, greater>> 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 BellmanFord(int start) { // checked // https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_1_B/judge/4817139/C++14 vector 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 q; vector 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 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 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 que; for(int i = 0; i < ver; i++) { if(num_input[i] == 0) { que.push(i); } } vector 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, 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 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, 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 RootToLeaf(int root) { // 0-indexed graph ret(ver); vector chk(ver, 0); chk[root] = 1; function 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 LeafToRoot(int root) { // 0-indexed graph ret(ver); vector chk(ver, 0); chk[root] = 1; function 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 par(int root) { // 0-indexed vector ret(ver, -1); ret[root] = root; // rootの親はroot function 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> ParentAndDistance(int root) { // 0-indexed vector> 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 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> GraphArray(void) { // chkecked // https://onlinejudge.u-aizu.ac.jp/status/users/Kite_kuma/submissions/1/GRL_1_C/judge/4817090/C++14 vector> ret(ver, vector(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 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 ret(ver); priority_queue, vector>, greater>> p; for(auto &e : edges[start]) { p.push(e); } vector 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 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 fir(ver, -1), sec(ver, -1); function 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 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 vector ReRootingDP(U &unit, function &merge, function &send, int root = 0) { auto tr = RootToLeaf(root); vector> v(ver); vector ret(ver); //求める答 function treeDP = [&](int now) { U res = unit; vector 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 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 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 ng, rg; // normal graph, reversed graph vector compo; // compo[i] = 新グラフでiが属する頂点集合番号 vector order; vector used; graph ret; // g:元のグラフ, ret:強連結成分分解後のグラフ template SCC(graph &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 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::max() / q < r + 10) continue; ll rev = r * q + y; if(rev % 10 == 0) continue; string s = to_string(rev); if(s.size() > 19) continue; if(s.size() == 19 && s.back() == '9') continue; reverse(all(s)); ll n = stoll(s); if(rev % q == y && n % p == x) { drop(n); } } return 0; }