using System; using System.Collections.Generic; using System.Linq; using System.IO; using System.Threading; using System.Text; using System.Text.RegularExpressions; using System.Diagnostics; using static util; using P = pair; class Program { static void Main(string[] args) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; var solver = new Solver(sw); // var t = new Thread(solver.solve, 1 << 28); // 256 MB // t.Start(); // t.Join(); solver.solve(); sw.Flush(); } } class Solver { StreamWriter sw; Scan sc; void Prt(string a) => sw.WriteLine(a); void Prt(IEnumerable a) => Prt(string.Join(" ", a)); void Prt(params object[] a) => Prt(string.Join(" ", a)); public Solver(StreamWriter sw) { this.sw = sw; this.sc = new Scan(); } public void solve() { long A, B, P, Q; sc.Multi(out A, out B, out P, out Q); var mat = new long[][]{ new long[]{ A, (M - B) % M }, new long[]{ 1, 0 } }; long H = 100003; var baby = new SortedDictionary(); { var p = new pair(P, Q); for (long b = 0; b < H; b++) { long hs = p.v1 * M + p.v2; if (!baby.ContainsKey(hs)) baby.Add(hs, b); else baby[hs] = b; p = new pair((p.v1 * mat[0][0] + p.v2 * mat[0][1]) % M, (p.v1 * mat[1][0] + p.v2 * mat[1][1]) % M); } } { var mp = new long[][]{ new long[]{ 1, 0 }, new long[]{ 0, 1 } }; for (int i = 0; i < H; ++i) { var nex = new long[2][]; nex[0] = new long[2]; nex[1] = new long[2]; nex[0][0] = (mp[0][0] * mat[0][0] + mp[0][1] * mat[1][0]) % M; nex[0][1] = (mp[0][0] * mat[0][1] + mp[0][1] * mat[1][1]) % M; nex[1][0] = (mp[1][0] * mat[0][0] + mp[1][1] * mat[1][0]) % M; nex[1][1] = (mp[1][0] * mat[0][1] + mp[1][1] * mat[1][1]) % M; mp = nex; } var p = new pair(A, 2); for (long a = 1; a <= H; a++) { p = new pair((p.v1 * mp[0][0] + p.v2 * mp[0][1]) % M, (p.v1 * mp[1][0] + p.v2 * mp[1][1]) % M); long hs = p.v1 * M + p.v2; if (baby.ContainsKey(hs)) { Prt(a * H - baby[hs] + 1); return; } } } Prt(-1); } } class pair : IComparable> { public T v1; public U v2; public pair() : this(default(T), default(U)) {} public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; } public int CompareTo(pair a) { int c = Comparer.Default.Compare(v1, a.v1); return c != 0 ? c : Comparer.Default.Compare(v2, a.v2); } public override string ToString() => $"{v1} {v2}"; public void Deconstruct(out T a, out U b) { a = v1; b = v2; } } static class util { // public static readonly int M = 1000000007; public static readonly int M = 998244353; public static readonly long LM = 1L << 60; public static readonly double eps = 1e-11; public static void DBG(string a) => Console.Error.WriteLine(a); public static void DBG(IEnumerable a) => DBG(string.Join(" ", a)); public static void DBG(params object[] a) => DBG(string.Join(" ", a)); public static void Assert(params bool[] conds) { if (conds.Any(x => !x)) throw new Exception(); } public static pair make_pair(T v1, U v2) => new pair(v1, v2); public static int CompareList(IList a, IList b) where T : IComparable { for (int i = 0; i < a.Count && i < b.Count; i++) if (a[i].CompareTo(b[i]) != 0) return a[i].CompareTo(b[i]); return a.Count.CompareTo(b.Count); } public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w; public static readonly int[] dd = { 0, 1, 0, -1 }; // static readonly string dstring = "RDLU"; public static IEnumerable

adjacents(int i, int j) { for (int k = 0; k < 4; k++) yield return new P(i + dd[k], j + dd[k ^ 1]); } public static IEnumerable

adjacents(int i, int j, int h, int w) { for (int k = 0; k < 4; k++) if (inside(i + dd[k], j + dd[k ^ 1], h, w)) yield return new P(i + dd[k], j + dd[k ^ 1]); } public static IEnumerable

adjacents(this P p) => adjacents(p.v1, p.v2); public static IEnumerable

adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w); public static IEnumerable all_subset(this int p) { for (int i = 0; ; i = i - p & p) { yield return i; if (i == p) break; } } public static Dictionary compress(this IEnumerable a) => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i); public static Dictionary compress(params IEnumerable[] a) => compress(a.SelectMany(x => x)); public static T[] inv(this Dictionary dic) { var res = new T[dic.Count]; foreach (var item in dic) res[item.Value] = item.Key; return res; } public static void swap(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; } public static void swap(this IList a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; } public static T[] copy(this IList a) { var ret = new T[a.Count]; for (int i = 0; i < a.Count; i++) ret[i] = a[i]; return ret; } } class Scan { StreamReader sr; public Scan() { sr = new StreamReader(Console.OpenStandardInput()); } public Scan(string path) { sr = new StreamReader(path); } public int Int => int.Parse(Str); public long Long => long.Parse(Str); public double Double => double.Parse(Str); public string Str => ReadLine.Trim(); public string ReadLine => sr.ReadLine(); public pair Pair() { T a; U b; Multi(out a, out b); return new pair(a, b); } public P P => Pair(); public int[] IntArr => StrArr.Select(int.Parse).ToArray(); public long[] LongArr => StrArr.Select(long.Parse).ToArray(); public double[] DoubleArr => StrArr.Select(double.Parse).ToArray(); public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries); bool eq() => typeof(T).Equals(typeof(U)); T ct(U a) => (T)Convert.ChangeType(a, typeof(T)); T cv(string s) => eq() ? ct(int.Parse(s)) : eq() ? ct(long.Parse(s)) : eq() ? ct(double.Parse(s)) : eq() ? ct(s[0]) : ct(s); public void Multi(out T a) => a = cv(Str); public void Multi(out T a, out U b) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); } public void Multi(out T a, out U b, out V c) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); } public void Multi(out T a, out U b, out V c, out W d) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); } public void Multi(out T a, out U b, out V c, out W d, out X e) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); } public void Multi(out T a, out U b, out V c, out W d, out X e, out Y f) { var ar = StrArr; a = cv(ar[0]); b = cv(ar[1]); c = cv(ar[2]); d = cv(ar[3]); e = cv(ar[4]); f = cv(ar[5]); } } static class MyMath { public static long Mod = util.M; // public static long Mod = 1000000007; public static bool isprime(long a) { if (a < 2) return false; for (long i = 2; i * i <= a; i++) if (a % i == 0) return false; return true; } public static bool[] sieve(int n) { var p = new bool[n + 1]; for (int i = 2; i <= n; i++) p[i] = true; for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false; return p; } public static int[] sieve2(int n) { var p = new int[n + 1]; for (int i = 2; i <= n; i++) p[i] = i; for (int i = 2; i * i <= n; i++) { if (p[i] == i) for (int j = i * i; j <= n; j += i) p[j] = Math.Min(p[j], i); } return p; } public static bool[] segmentSieve(long l, long r) { int sqn = (int)Math.Sqrt(r + 9); var ps = getprimes(sqn); return segmentSieve(l, r,ps); } public static bool[] segmentSieve(long l, long r, List ps) { var sieve = new bool[r - l + 1]; for (long i = l; i <= r; i++) sieve[i - l] = true; foreach (long p in ps) { if (p * p > r) break; for (long i = p >= l ? p * p : (l + p - 1) / p * p; i <= r; i += p) sieve[i - l] = false; } return sieve; } public static List getprimes(int n) { var prs = new List(); var p = sieve(n); for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i); return prs; } public static long pow(long a, long b, long mod) { a %= mod; if (b < 0) Console.Error.WriteLine($"power number is negative ({a}^{b})."); if (b <= 0) return 1; var t = pow(a, b / 2, mod); if ((b & 1) == 0) return t * t % mod; return t * t % mod * a % mod; } public static long pow(long a, long b) => pow(a, b, Mod); public static long inv(long a) => pow(a, Mod - 2); public static long gcd(long a, long b) { while (b > 0) { var t = a % b; a = b; b = t; } return a; } // a x + b y = gcd(a, b) public static long extgcd(long a, long b, out long x, out long y) { long g = a; x = 1; y = 0; if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; } return g; } // return (r, m): x = r (mod. m) // return (0, -1) if no answer public static pair chineserem(IList b, IList m) { long r = 0, M = 1; for (int i = 0; i < b.Count; ++i) { long p, q; long d = extgcd(M, m[i], out p, out q); // p is inv of M/d (mod. m[i]/d) if ((b[i] - r) % d != 0) return new pair(0, -1); long tmp = (b[i] - r) / d * p % (m[i]/d); r += M * tmp; M *= m[i]/d; } return new pair((r % M + M) % M, M); } // return k: x^k = y (mod. mod) O(sqrt(mod)) public static long modlog(long x, long y, long mod) { if (y == 1) return 0; long H = (long)Math.Sqrt(mod) + 1; var baby = new Dictionary(); for (long b = 0, xby = y; b < H; b++, xby = (xby * x) % mod) { if (!baby.ContainsKey(xby)) baby.Add(xby, b); else baby[xby] = b; } long xH = 1; for (int i = 0; i < H; ++i) xH = xH * x % mod; for (long a = 1, xaH = xH; a <= H; a++, xaH = (xaH * xH) % mod) if (baby.ContainsKey(xaH)) return a * H - baby[xaH]; return -1; } public static long lcm(long a, long b) => a / gcd(a, b) * b; static long[] facts, invs; public static void setfacts(int n) { facts = new long[n + 1]; facts[0] = 1; for (int i = 1; i <= n; i++) facts[i] = facts[i - 1] * i % Mod; invs = new long[n + 1]; invs[n] = inv(facts[n]); for (int i = n; i > 0 ; i--) invs[i - 1] = invs[i] * i % Mod; } public static long fact(long n) { if (n < 0) return 0; if (facts != null && facts.Length > n) return facts[n]; long numer = 1; for (long i = 1; i <= n; i++) numer = numer * (i % Mod) % Mod; return numer; } public static long perm(long n, long r) { if (n < 0 || r < 0 || r > n) return 0; if (facts != null && facts.Length > n) return facts[n] * invs[n - r] % Mod; long numer = 1; for (long i = 0; i < r; i++) numer = numer * ((n - i) % Mod) % Mod; return numer; } public static long comb(long n, long r) { if (n < 0 || r < 0 || r > n) return 0; if (facts != null && facts.Length > n) return facts[n] * invs[r] % Mod * invs[n - r] % Mod; if (n - r < r) r = n - r; long numer = 1, denom = 1; for (long i = 0; i < r; i++) { numer = numer * ((n - i) % Mod) % Mod; denom = denom * ((i + 1) % Mod) % Mod; } return numer * inv(denom) % Mod; } public static long multi_choose(long n, long r) { if (n == 0 && r == 0) return 1; else return comb(n + r - 1, r); } public static long[][] getcombs(int n) { var ret = new long[n + 1][]; for (int i = 0; i <= n; i++) { ret[i] = new long[i + 1]; ret[i][0] = ret[i][i] = 1; for (int j = 1; j < i; j++) ret[i][j] = (ret[i - 1][j - 1] + ret[i - 1][j]) % Mod; } return ret; } // nC0, nC2, ..., nCn public static long[] getcomb(int n) { // var ret = new long[n + 1]; // ret[0] = 1; // for (int i = 0; i < n; i++) ret[i + 1] = ret[i] * (n - i) % Mod * inv(i + 1) % Mod; // return ret; if (facts == null || facts.Length <= n) setfacts(n); var res = new long[n + 1]; for (int i = 0; i < n + 1; i++) res[i] = comb(n, i); return res; } }