import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop, core.stdc.stdlib; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } // floor(a^(1/k)) ulong floorKthRoot(ulong a, ulong k) { import core.bitop : bsr; import std.algorithm : min; if (a == 0) { return 0; } else if (k <= 1) { return a; } else if (k == 2) { ulong b = a, x = 0, y = 0; for (int e = bsr(a) & ~1; e >= 0; e -= 2) { x <<= 1; y <<= 1; if (b >= (y | 1) << e) { b -= (y | 1) << e; x |= 1; y += 2; } } return x; } else if (k <= 40) { // min x s.t. x^k >= 2^64 enum ulong[] HIS = [0, 0, 4294967296UL, 2642246, 65536, 7132, 1626, 566, 256, 139, 85, 57, 41, 31, 24, 20, 16, 14, 12, 11, 10, 9, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4]; ulong lo = 1UL << (bsr(a) / k); ulong hi = min(1UL << (bsr(a) / k + 1), HIS[cast(size_t)(k)]); for (; lo + 1 < hi; ) { const ulong mid = (lo + hi) / 2; ulong b = mid * mid; foreach (i; 2 .. k) b *= mid; ((b <= a) ? lo : hi) = mid; } return lo; } else if (k <= 63) { return ((1UL << k) <= a) ? 2 : 1; } else { return 1; } } // a^-1 (mod m) long modInv(long a, long m) in { assert(m > 0, "modInv: m > 0 must hold"); } do { long b = m, x = 1, y = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1"); if (b == -1) y = -y; return (y < 0) ? (y + m) : y; } x -= t * y; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1"); if (a == -1) x = -x; return (x < 0) ? (x + m) : x; } y -= t * x; } } Int mod(Int)(Int a, Int m) { if ((a %= m) < 0) a += m; return a; } Int gcd(Int)(Int a, Int b) { return (b != 0) ? gcd(b, a % b) : a; } Int lcm(Int)(Int a, Int b) { return a / gcd(a, b) * b; } Int gojo(Int)(Int a, Int b, out Int x, out Int y) { if (b != 0) { Int g = gojo(b, a % b, y, x); y -= (a / b) * x; return g; } x = 1; y = 0; return a; } Int modInv(Int)(Int a, Int m) { Int x, y; gojo(a, m, x, y); return mod(x, m); } long modLogP(long a, long b, long m) { a = mod(a, m); b = mod(b, m); if (m == 1) return 0; long k, al = 1; Tuple!(long,long)[] as; for (k = 0; k * k < m; ++k) { as ~= tuple(al, k); al = (al * a) % m; } as.sort; al = modInv(al, m); for (long i = 0; i < k; ++i) { int pos = as.lowerBound(tuple(b, 0L)); if (pos < as.length && as[pos][0] == b) return i * k + as[pos][1]; b = (b * al) % m; } return -1; } long P; long[][] A, B; long[][] div(long[][] a, long t) { const invT = modInv(t, P); auto b = new long[][](2, 2); foreach (i; 0 .. 2) foreach (j; 0 .. 2) { b[i][j] = mod(invT * a[i][j], P); } return b; } long[][] inv(long[][] a) { const det = mod(a[0][0] * a[1][1] - a[0][1] * a[1][0], P); return div([[a[1][1], -a[0][1]], [-a[1][0], a[0][0]]], det); } long[][] mul(long[][] a, long[][] b) { auto c = new long[][](2, 2); foreach (i; 0 .. 2) foreach (k; 0 .. 2) foreach (j; 0 .. 2) { c[i][j] = mod(c[i][j] + a[i][k] * b[k][j], P); } return c; } long[][] power(long[][] a, long e) { long[][] b = a, c = [[1, 0], [0, 1]]; for (; e; e >>= 1) { if (e & 1) c = mul(c, b); b = mul(b, b); } return c; } long solveBSGS(long[][] a, long[][] b) { const m = cast(int)(floorKthRoot(2 * P, 2) + 2); auto als = new Tuple!(long[][], int)[m]; long[][] al = [[1, 0], [0, 1]]; foreach (l; 0 .. m) { als[l] = tuple(al, l); al = mul(al, a); } als.sort; al = inv(al); long[][] amk = b; foreach (k; 0 .. m) { const pos = als.lowerBound(tuple(amk, 0)); if (pos < m && als[pos][0] == amk) { return k * cast(long)(m) + als[pos][1]; } amk = mul(amk, al); } return -1; } void main() { try { for (; ; ) { P = readLong(); A = new long[][](2, 2); foreach (i; 0 .. 2) foreach (j; 0 .. 2) { A[i][j] = readLong(); } B = new long[][](2, 2); foreach (i; 0 .. 2) foreach (j; 0 .. 2) { B[i][j] = readLong(); } long ans; const detA = mod(A[0][0] * A[1][1] - A[0][1] * A[1][0], P); const detB = mod(B[0][0] * B[1][1] - B[0][1] * B[1][0], P); if (detA == 0) { if (detB == 0) { if (A == [[0, 0], [0, 0]]) { if (B == [[0, 0], [0, 0]]) { ans = 1; } else { ans = -1; } } else { /* C^-1 A C = [[r, 0], [0, 0]] a00 c00 + a01 c10 = r c00 a10 c00 + a11 c10 = r c10 a00 c01 + a01 c11 = 0 a10 c01 + a11 c11 = 0 */ const r = mod(A[0][0] + A[1][1], P); if(r==0)exit(1); assert(r != 0); auto c = new long[][](2, 2); c[0][0] = mod(-A[0][1], P); c[1][0] = mod(A[0][0] - r, P); if (c[0][0] == 0 && c[1][0] == 0) { c[0][0] = mod(-(A[1][1] - r), P); c[1][0] = mod(A[1][0], P); } if (c[0][0] == 0 && c[1][0] == 0) { assert(false); } c[0][1] = mod(-A[0][1], P); c[1][1] = mod(A[0][0], P); if (c[0][1] == 0 && c[1][1] == 0) { c[0][1] = mod(-A[1][1], P); c[1][1] = mod(A[1][0], P); } if (c[0][1] == 0 && c[1][1] == 0) { assert(false); } debug { writeln("r = ", r); writeln("c = ", c); } auto a = mul(mul(inv(c), A), c); auto b = mul(mul(inv(c), B), c); debug { writeln("a = ", a); writeln("b = ", b); } assert(a == [[r, 0L], [0L, 0L]]); if (b[0][1] == 0 && b[1][0] == 0 && b[1][1] == 0) { const res = modLogP(r, mod(b[0][0] * modInv(r, P), P), P); if (res == -1) { // exit(1); ans = -1; } else { ans = res + 1; } } else { ans = -1; } } } else { ans = -1; } } else { const period = modLogP(detA, modInv(detA, P), P) + 1; long e0 = modLogP(detA, detB, P); debug { writeln("detA = ", detA, ", detB = ", detB); writeln("period = ", period); writeln("e0 = ", e0); } if (e0 == -1) { ans = -1; } else { if (e0 == 0) { e0 += period; } auto a = power(A, period); auto b = mul(B, inv(power(A, e0))); debug { writeln("a = ", a); writeln("b = ", b); } const res = solveBSGS(a, b); if (res == -1) { ans = -1; } else { ans = e0 + period * res; } } } writeln(ans); } } catch (EOFException e) { } }