// URL: https://yukicoder.me/problems/no/187 import std.algorithm, std.array, std.bitmanip, std.container, std.conv, std.format, std.functional, std.math, std.range, std.traits, std.typecons, std.stdio, std.string; version(unittest) {} else void main() { int N; io.getV(N); int[] X, Y; io.getC(N, X, Y); auto x = GmpInt(X[0]), y = GmpInt(Y[0]); foreach (i; 1..N) if (!calc(x, y, GmpInt(X[i]), GmpInt(Y[i]))) io.put!"{exit: true}"(-1); auto mod = 10^^9+7; io.putB(x == 0, y%mod, x%mod); } auto calc(T)(ref T X1, ref T Y1, T X2, T Y2) { auto r = extGcd(Y1, Y2); if ((X2-X1)%r.gcd != 0) return false; auto y1 = Y1/r.gcd, y2 = Y2/r.gcd; Y1 = y1*y2*r.gcd; X1 = pmod(r.x*y1*(X2-X1)+X1, Y1); return true; } pure nothrow @nogc @safe { auto lowerBoundBy(alias conv = "a", alias comp = "a tuple(e, convFun(e))).assumeSorted!((a, b) => compFun(a[1], b[1])); } } pure nothrow @nogc @safe { T cdiv(T)(const T a, const T b) { return (a+b-1)/b; } T pmod(T)(const T a, const T b) { return a >= 0 ? a%b : a%b+b; } ExtGcdResult!T extGcd(T)(const T a, const T b) { if (a == 0) { return ExtGcdResult!T(T(b), T(0), T(1)); } else { auto r = extGcd(b%a, a); return ExtGcdResult!T(r.gcd, r.y-(b/a)*r.x, r.x); } } private struct ExtGcdResult(T) { T gcd, x, y; } } struct GmpInt { pure nothrow @nogc @safe { this(long v) { __gmpz_init_set_si(&z, v); } this(ref return scope const GmpInt v) { __gmpz_init_set(&z, &v.z); } ~this() { __gmpz_clear(&z); } long toLong() const { return __gmpz_get_si(&z); } bool opEquals(const GmpInt v) const { return __gmpz_cmp(&z, &v.z) == 0; } bool opEquals(T)(T v) const if (isIntegral!T) { return __gmpz_cmp_si(&z, v) == 0; } int opCmp(const GmpInt v) const { return __gmpz_cmp(&z, &v.z); } int opCmp(T)(T v) const if (isIntegral!T) { return __gmpz_cmp_si(&z, v); } ref GmpInt opAssign(const GmpInt v) { __gmpz_init_set(&z, &v.z); return this; } ref GmpInt opAssign(T)(T v) if (isIntegral!T) { __gmpz_init_set_si(&z, v); return this; } GmpInt opBinary(string op)(const GmpInt v) const if (op == "+" || op == "-" || op == "*" || op == "/" || op == "%") { auto r = GmpInt(0); static if (op == "+") __gmpz_add(&r.z, &z, &v.z); else static if (op == "-") __gmpz_sub(&r.z, &z, &v.z); else static if (op == "*") __gmpz_mul(&r.z, &z, &v.z); else static if (op == "/") __gmpz_tdiv_q(&r.z, &z, &v.z); else static if (op == "%") __gmpz_tdiv_r(&r.z, &z, &v.z); return r; } ref GmpInt opOpAssign(string op)(const GmpInt v) if (op == "+" || op == "-" || op == "*" || op == "/" || op == "%") { static if (op == "+") __gmpz_add(&z, &z, &v.z); else static if (op == "-") __gmpz_sub(&z, &z, &v.z); else static if (op == "*") __gmpz_mul(&z, &z, &v.z); else static if (op == "/") __gmpz_tdiv_q(&z, &z, &v.z); else static if (op == "%") __gmpz_tdiv_r(&z, &z, &v.z); return this; } GmpInt opBinary(string op, U)(U v) const if ((op == "+" || op == "-" || op == "*" || op == "/" || op == "%" || op == "^^") && isIntegral!U) { auto r = GmpInt(0); static if (op == "+") __gmpz_add_ui(&r.z, &z, v); else static if (op == "-") __gmpz_sub_ui(&r.z, &z, v); else static if (op == "*") __gmpz_mul_ui(&r.z, &z, v); else static if (op == "/") __gmpz_tdiv_q_ui(&r.z, &z, v); else static if (op == "%") __gmpz_tdiv_r_ui(&r.z, &z, v); else static if (op == "^^") __gmpz_pow_ui(&r.z, &z, v); return r; } ref GmpInt opOpAssign(string op, U)(U v) if ((op == "+" || op == "-" || op == "*" || op == "/" || op == "%" || op == "^^") && isIntegral!U) { static if (op == "+") __gmpz_add_ui(&z, &z, v); else static if (op == "-") __gmpz_sub_ui(&z, &z, v); else static if (op == "*") __gmpz_mul_ui(&z, &z, v); else static if (op == "/") __gmpz_tdiv_q_ui(&z, &z, v); else static if (op == "%") __gmpz_tdiv_r_ui(&z, &z, v); else static if (op == "^^") __gmpz_pow_ui(&z, &z, v); return this; } GmpInt abs() const { auto r = GmpInt(0); __gmpz_abs(&r.z, &z); return r; } GmpInt sqrt() const { auto r = GmpInt(0); __gmpz_sqrt(&r.z, &z); return r; } size_t popcnt() const { return __gmpz_popcount(&z); } bool probabPrime(int reps = 20) const { return __gmpz_probab_prime_p(&z, reps) != 0; } } pure nothrow { @safe this(string s, int base = 10) { __gmpz_init_set_str(&z, s.toStringz, base); } @trusted string toString(int base = 10) const { auto sz = __gmpz_sizeinbase(&z, base); auto buf = new char[](sz + 2); __gmpz_get_str(buf.ptr, base, &z); return buf.ptr.fromStringz.to!string; } } size_t fprint(File f, int base = 10) const { return __gmpz_out_str(f.getFP, base, &z); } private { import std.stdio : File; __mpz_struct z; } } extern(C) pragma(inline, false) { import core.stdc.stdio : FILE; alias __mp_limb_t = ulong; struct __mpz_struct { int _mp_alloc; int _mp_size; __mp_limb_t* _mp_d; } alias mpz_srcptr = const(__mpz_struct)*; alias mpz_ptr = __mpz_struct*; pure nothrow @nogc @safe { void __gmpz_init(mpz_ptr); void __gmpz_clear(mpz_ptr); void __gmpz_init_set(mpz_ptr, mpz_srcptr); void __gmpz_init_set_si(mpz_ptr, long); int __gmpz_init_set_str(mpz_ptr, const char*, int); void __gmpz_set(mpz_ptr, mpz_srcptr); void __gmpz_set_si(mpz_ptr, long); long __gmpz_get_si(mpz_srcptr); char *__gmpz_get_str(char*, int, mpz_srcptr); size_t __gmpz_sizeinbase(mpz_srcptr, int); size_t __gmpz_out_str(FILE*, int, mpz_srcptr); int __gmpz_cmp(mpz_srcptr, mpz_srcptr); int __gmpz_cmp_si(mpz_srcptr, long); void __gmpz_add(mpz_ptr, mpz_srcptr, mpz_srcptr); void __gmpz_add_ui(mpz_ptr, mpz_srcptr, ulong); void __gmpz_sub(mpz_ptr, mpz_srcptr, mpz_srcptr); void __gmpz_sub_ui(mpz_ptr, mpz_srcptr, ulong); void __gmpz_mul(mpz_ptr, mpz_srcptr, mpz_srcptr); void __gmpz_mul_ui(mpz_ptr, mpz_srcptr, ulong); void __gmpz_tdiv_q(mpz_ptr, mpz_srcptr, mpz_srcptr); void __gmpz_tdiv_r(mpz_ptr, mpz_srcptr, mpz_srcptr); ulong __gmpz_tdiv_q_ui(mpz_ptr, mpz_srcptr, ulong); ulong __gmpz_tdiv_r_ui(mpz_ptr, mpz_srcptr, ulong); void __gmpz_pow_ui(mpz_ptr, mpz_srcptr, ulong); void __gmpz_abs(mpz_ptr, mpz_srcptr); void __gmpz_sqrt(mpz_ptr, mpz_srcptr); size_t __gmpz_popcount(mpz_srcptr); int __gmpz_probab_prime_p(mpz_srcptr, int reps); } } pragma(lib, "gmp"); auto io = IO!()(); import std.stdio; struct IO(alias IN = stdin, alias OUT = stdout) { import std.meta : allSatisfy; import core.stdc.stdlib : exit; void getV(T...)(ref T v) { foreach (ref w; v) get(w); } void getA(T)(size_t n, ref T v) if (hasAssignableElements!T) { v = new T(n); foreach (ref w; v) get(w); } void getC(T...)(size_t n, ref T v) if (allSatisfy!(hasAssignableElements, T)) { foreach (ref w; v) w = new typeof(w)(n); foreach (i; 0..n) foreach (ref w; v) get(w[i]); } void getM(T)(size_t r, size_t c, ref T v) if (hasAssignableElements!T && hasAssignableElements!(ElementType!T)) { v = new T(r); foreach (ref w; v) getA(c, w); } template getS(E...) { void getS(T)(size_t n, ref T v) { v = new T(n); foreach (ref w; v) foreach (e; E) mixin("get(w."~e~");"); } } const struct PutConf { bool newline = true, flush, exit; string floatFormat = "%.10f", delimiter = " "; } void put(alias conf = "{}", T...)(T v) { mixin("const PutConf c = "~conf~"; putMain!c(v);"); } void putB(alias conf = "{}", S, T)(bool c, S t, T f) { if (c) put!conf(t); else put!conf(f); } void putRaw(T...)(T v) { OUT.write(v); OUT.writeln; } private { dchar[] buf; auto sp = (new dchar[](0)).splitter; void nextLine() { IN.readln(buf); sp = buf.splitter; } void get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); } void putMain(PutConf c, T...)(T v) { foreach (i, w; v) { putOne!c(w); if (i+1 < v.length) OUT.write(c.delimiter); } static if (c.newline) OUT.writeln; static if (c.flush) OUT.flush(); static if (c.exit) exit(0); } void putOne(PutConf c, T)(T v) { static if (isInputRange!T && !isSomeString!T) putRange!c(v); else static if (isFloatingPoint!T) OUT.write(format(c.floatFormat, v)); else static if (hasMember!(T, "fprint")) v.fprint(OUT); else OUT.write(v); } void putRange(PutConf c, T)(T v) { auto w = v; while (!w.empty) { putOne!c(w.front); w.popFront(); if (!w.empty) OUT.write(c.delimiter); } } } }