#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif template lint power(lint x, lint n, lint MOD) { lint ans = 1; while (n>0) { if (n & 1) (ans *= x) %= MOD; (x *= x) %= MOD; n >>= 1; } return ans; } lint md(string s, lint x) { lint ret = 0; for (auto c : s) { ret = (ret * 10 + c - '0') % x; } return ret; } lint inv(lint x) { lint ret = 0; while (x) { ret = ret * 10 + x % 10; x /= 10; } return ret; } constexpr lint P = 90007; string solve(lint Q, lint x, lint y) { assert(Q != 70009); lint yinv = inv(y); lint md = yinv % P; string ret = to_string(yinv); while (md % P != x) { md = (md * 10) % P; ret += "0"; } return ret; // unordered_map mds; // FOR(T, 1, 2000000) { // const lint k = x + P * lint(T); // assert(k % P == x); // lint y_ = inv(k) % Q; // if (y_ == y) { // dbg(k); // return to_string(k); // } // mds[y_] = k; // } // dbg("OK"); // __int128 inv10 = power<__int128>(10, Q - 2, Q); // __int128 cur = ((y - 70009) % Q + Q) % Q; // string ans; // FOR(t, 1, 90000) { // cur = cur * inv10 % Q; // if (t >= 5 and mds.count(cur)) { // dbg(t); // ans += to_string(P); // ans += string(t - 5, '0'); // ans += to_string(mds.at(cur)); // assert(md(ans, P) == x); // auto ansrev = ans; // reverse(ALL(ansrev)); // assert(md(ansrev, Q) == y); // return ans; // } // } // // throw; // return ""; } int main() { // dbg(inv(500030)); // FOR(x, 1, 10) { // FOR(y, 1, 10) { // if (y < 2) solve(2, x, y); // if (y < 3) solve(3, x, y); // if (y < 5) solve(5, x, y); // if (y < 7) solve(7, x, y); // solve(90007, x, y); // } // } lint Q, x, y; cin >> Q >> Q >> x >> y; cout << solve(Q, x, y) << '\n'; }