// URL: https://yukicoder.me/problems/no/195 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() { long[] X; io.getA(3, X); X = X.sort.uniq.array; auto n = 41, c = new long[](n), d = new long[](n); c[0] = 1; d[0] = 0; auto m = matrix([[0, 1], [1, 1]]); foreach (i; 1..n) { auto mi = m^^(i-1); c[i] = mi[1][0]; d[i] = mi[1][1]; } auto r = [10L^^18, 10L^^18]; if (X.length == 1) { if (X[0] == 1) io.put!"{exit: true}"(1, 1); auto A = 1L; foreach (i; 1..n) { auto B = frac(X[0]-A*c[i], d[i]); if (B.b == 1 && B.a > 0) r.minU([A, B.a]); } } else if (X.length == 2) { foreach (i; 0..n) foreach (j; i+1..n) { auto A = frac(d[j]*X[0]-d[i]*X[1], c[i]*d[j]-d[i]*c[j]); auto B = frac(c[i]*X[1]-c[j]*X[0], c[i]*d[j]-d[i]*c[j]); if (A.b == 1 && A.a > 0 && B.b == 1 && B.a > 0) r.minU([A.a, B.a]); } } else { foreach (i; 0..n) foreach (j; i+1..n) { auto A = frac(d[j]*X[0]-d[i]*X[1], c[i]*d[j]-d[i]*c[j]); auto B = frac(c[i]*X[1]-c[j]*X[0], c[i]*d[j]-d[i]*c[j]); if (A.b == 1 && A.a > 0 && B.b == 1 && B.a > 0) { auto a = A.a, b = B.a; foreach (k; j+1..n) if (c[k]*a+d[k]*b == X[2]) r.minU([a, b]); } } } io.putB(r[0] < 10L^^18 && r[1] < 10L^^18, r, -1); } pragma(inline) { pure nothrow @nogc @safe { T minU(T, U)(ref T a, U b) { return a = min(a, b); } T maxU(T, U)(ref T a, U b) { return a = max(a, b); } } } struct Frac(T) { import std.numeric : gcd; T a, b; pure nothrow @nogc @safe { this(T a, T b) in { assert(b != 0); } do { this.a = a; this.b = b; } bool opEquals(Frac!T r) const { return (a == 0 && r.a == 0) || (a == r.a && b == r.b); } int opCmp(Frac!T r) const { return a*r.br.a*b ? 1 : 0; } Frac!T inv() in { assert(a != 0); } do { return Frac!T(b, a).normalizeSign; } Frac!T opUnary(string op: "-")() { return Frac!T(-a, b); } Frac!T opBinary(string op)(Frac!T r) if (op == "+" || op == "-") { auto g = gcd(b, r.b); return Frac!T(mixin("r.b/g*a"~op~"b/g*r.a"), b/g*r.b).reduction(); } Frac!T opOpAssign(string op)(Frac!T r) if (op == "+" || op == "-") { auto g = gcd(b, r.b); a = mixin("r.b/g*a"~op~"b/g*r.a"); b = b/g*r.b; return reduction(); } Frac!T opBinary(string op: "*")(Frac!T r) { auto g1 = gcd(a.abs, r.b), g2 = gcd(r.a.abs, b); return Frac!T((a/g1)*(r.a/g2), (b/g2)*(r.b/g1)); } ref Frac!T opOpAssign(string op: "*")(Frac!T r) { auto g1 = gcd(a.abs, r.b), g2 = gcd(r.a.abs, b); a = (a/g1)*(r.a/g2); b = (b/g2)*(r.b/g1); return this; } Frac!T opBinary(string op: "/")(Frac!T r) in { assert(r.b != 0); } do { auto g1 = gcd(a.abs, r.a.abs), g2 = gcd(b, r.b); return Frac!T((a/g1)*(r.b/g2), (b/g2)*(r.a/g1)).normalizeSign(); } ref Frac!T opOpAssign(string op: "/")(Frac!T r) in { assert(r.b != 0); } do { auto g1 = gcd(a.abs, r.a.abs), g2 = gcd(b, r.b); a = (a/g1)*(r.b/g2); b = (b/g2)*(r.a/g1); return normalizeSign(); } private { ref Frac!T reduction() { auto g = gcd(a.abs, b); a /= g; b /= g; return this; } ref Frac!T normalizeSign() { if (b < 0) { a = -a; b = -b; } return this; } } } } pure nothrow @nogc @safe { Frac!T frac(T)(T a, T b) { return Frac!T(a, b).normalizeSign().reduction(); } } pure nothrow @safe { T powr(alias pred = "a*b", T, U)(const T a, U n, T one) if (isIntegral!U) { auto b = T(a); alias predFun = binaryFun!pred; if (n == 0) return one; auto r = one; for (; n > 0; n >>= 1) { if (n&1) r = predFun(r, b); b = predFun(b, b); } return r; } T powr(alias pred = "a*b", T, U)(const T a, U n) if (isIntegral!U) { return powr!(pred, T, U)(a, n, T(1)); } } struct Vector(T) { size_t n; @property T[] array() { return a; } alias array this; pure nothrow @safe { this(size_t n, T zero = T(0)) in { assert(n > 0); } do { this.n = n; this.zero = zero; a = new T[](n); if (T.init != zero) foreach (i; 0..n) a[i] = zero; } this(U)(U[] b, T zero = T(0)) in { assert(b.length > 0); } do { n = b.length; this.zero = zero; static if (is(T == U)) { a = b; } else { a = new T[](n); foreach (i; 0..n) a[i] = b[i]; } } this(ref return scope const Vector!T v) { n = v.n; zero = v.zero; a = new T[](n); foreach (i; 0..n) a[i] = v.a[i]; } Vector!T dup() const { return Vector!T(this); } Vector!T opBinary(string op)(const Vector!T b) const if (op == "+" || op == "-") in { assert(n == b.n); } do { auto x = Vector!T(n, zero); foreach (i; 0..n) x[i] = mixin("a[i]"~op~"b.a[i]"); return x; } ref Vector!T opOpAssign(string op)(const Vector!T b) if (op == "+" || op == "-") in { assert(n == b.n); } do { foreach (i; 0..n) mixin("a[i]"~op~"=b.a[i];"); return this; } Vector!T opBinary(string op: "*", U)(U b) const if (isNumeric!T) { auto x = Vector!T(n, zero); foreach (i; 0..n) x[i] = a[i]*b; return x; } ref Vector!T opOpAssign(string op: "*", U)(U b) if (isNumeric!T) { foreach (i; 0..n) a[i] *= b; return this; } T opBinary(string op: "*")(const Vector!T b) const in { assert(n == b.n); } do { auto x = T(zero); foreach (i; 0..n) x += a[i]*b.a[i]; return x; } } private { T[] a; T zero; } } pure nothrow @safe { auto vector(T)(T[] a, T zero = T(0)) { return Vector!T(a, zero); } T hypot2(T)(const Vector!T a) { return a*a; } pure Vector!T cross(T)(Vector!T a, Vector!T b) in { assert(a.n == 3 && b.n == 3); } do { return Vector!T([a[1]*b[2]-a[2]*b[1], a[2]*b[0]-a[0]*b[2], a[0]*b[1]-a[1]*b[0]], a.zero); } } struct Matrix(T) { size_t r, c; @property T[][] array() { return a; } alias array this; pure nothrow @safe { static Matrix!T unit(size_t n, T zero = T(0), T one = T(1)) in { assert(n > 0); } do { auto r = Matrix!T(n, n, zero, one); foreach (i; 0..n) r[i][i] = one; return r; } this(size_t r, size_t c, T zero = T(0), T one = T(1)) in { assert(r > 0 && c > 0); } do { this.r = r; this.c = c; this.zero = zero; this.one = one; a = new T[][](r, c); if (T.init != zero) foreach (i; 0..r) foreach (j; 0..c) a[i][j] = zero; } this(U)(U[][] b, T zero = T(0), T one = T(1)) in { assert(b.length > 0 && b[0].length > 0 && b.all!(l => l.length == b[0].length)); } do { r = b.length; c = b[0].length; this.zero = zero; this.one = one; static if (is(T == U)) { a = b; } else { a = new T[][](r, c); foreach (i; 0..r) foreach (j; 0..c) a[i][j] = b[i][j]; } } this(ref return scope const Matrix!T v) { r = v.r; c = v.c; zero = v.zero; one = v.one; a = new T[][](r, c); foreach (i; 0..r) foreach (j; 0..c) a[i][j] = v.a[i][j]; } Matrix!T dup() const { return Matrix!T(this); } bool opEquals(Matrix!T b) const { return r == b.r && c == b.c && zip(a, b.a).all!"a[0]==a[1]"; } Matrix!T opBinary(string op)(const Matrix!T b) const if (op == "+" || op == "-") in { assert(r == b.r && c == b.c); } do { auto x = Matrix!T(r, c, zero, one); foreach (i; 0..r) foreach (j; 0..c) x[i][j] = mixin("a[i][j]"~op~"b.a[i][j]"); return x; } ref Matrix!T opOpAssign(string op)(const Matrix!T b) if (op == "+" || op == "-") in { assert(r == b.r && c == b.c); } do { foreach (i; 0..r) foreach (j; 0..c) mixin("a[i][j]"~op~"=b.a[i][j];"); return this; } Matrix!T opBinary(string op: "*", U)(U b) const if (isNumeric!U) { auto x = Matrix!T(r, c, zero, one); foreach (i; 0..r) foreach (j; 0..c) x[i][j] = a[i][j]*b; return x; } ref Matrix!T opOpAssign(string op: "*", U)(U b) if (isNumeric!U) { foreach (i; 0..r) foreach (j; 0..c) a[i][j] *= b; return this; } Matrix!T opBinary(string op: "*")(const Matrix!T b) const in { assert(c == b.r); } do { auto x = Matrix!T(r, b.c, zero, one); foreach (i; 0..r) foreach (j; 0..b.c) foreach (k; 0..c) x[i][j] += a[i][k]*b.a[k][j]; return x; } ref Matrix!T opOpAssign(string op: "*")(const Matrix!T b) in { assert(c == b.r); } do { auto x = this*b; r = x.r; c = x.c; a = x.a; return this; } Vector!T opBinary(string op: "*")(const Vector!T b) const in { assert(c == b.n); } do { auto x = Vector!T(r, zero); foreach (i; 0..r) foreach (j; 0..c) x[i] += a[i][j]*b.a[j]; return x; } Matrix!T opBinary(string op: "^^", U)(U n) const if (isIntegral!U) in { assert(r == c); } do { return powr(this, n, Matrix!T.unit(r, zero, one)); } } private { T[][] a; T zero, one; } } pure nothrow @safe { auto matrix(T)(T[][] a, T zero = T(0), T one = T(1)) { return Matrix!T(a, zero, one); } T det(T)(Matrix!T a) in { assert(a.r == a.c); } do { auto n = a.r, b = a.dup, d = a.one; foreach (i; 0..n) { auto p = i; foreach (j; i+1..n) if (b[p][i].abs < b[j][i].abs) p = j; swap(b[p], b[i]); foreach (j; i+1..n) foreach (k; i+1..n) b[j][k] -= b[i][k]*b[j][i]/b[i][i]; d *= b[i][i]; if (p != i) d = -d; } return d; } } 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); } } } }