// URL: https://yukicoder.me/problems/no/195 import std.algorithm, std.array, std.container, std.math, std.range, std.typecons, 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 = min(r, [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 = min(r, [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 = min(r, [a, b]); } } } io.putB(r[0] < 10L^^18 && r[1] < 10L^^18, r, -1); } struct Frac(T) { import std.numeric; alias F = Frac!T, Op = string; T a, b; this(T a, T b) in { assert(b != 0); } do { this.a = a; this.b = b; } pure bool opEquals(F r) { return a == 0 && r.a == 0 || a == r.a && b == r.b; } pure int opCmp(F r) { return a*r.br.a*b ? 1 : 0; } pure F inv() in { assert(a != 0); } do { return F(b, a).normalizeSign; } pure F opUnary(Op op: "-")() { return F(-a, b); } pure F opBinary(Op op)(F r) if (op=="+"||op=="-") { auto g = gcd(b, r.b); return F(mixin("r.b/g*a"~op~"b/g*r.a"), b/g*r.b).reduction(); } ref F opOpAssign(Op op)(F 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(); } pure F opBinary(Op op: "*")(F r) { auto g1 = gcd(a.abs, r.b), g2 = gcd(r.a.abs, b); return F((a/g1)*(r.a/g2), (b/g2)*(r.b/g1)); } ref F opOpAssign(Op op: "*")(F 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; } pure F opBinary(Op op: "/")(F r) in { assert(r.b != 0); } do { auto g1 = gcd(a.abs, r.a.abs), g2 = gcd(b, r.b); return F((a/g1)*(r.b/g2), (b/g2)*(r.a/g1)).normalizeSign(); } ref F opOpAssign(Op op: "/")(F 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 F reduction() { auto g = gcd(a.abs, b); a /= g; b /= g; return this; } ref F normalizeSign() { if (b < 0) { a = -a; b = -b; } return this; } } } auto frac(T)(T a, T b) { return Frac!T(a, b).normalizeSign().reduction(); } alias me = MatrixElement!int, Matrix = me.Matrix; auto lowerBoundBy(alias conv = "a", alias comp = "a tuple(e, convFun(e))).assumeSorted!((a, b) => compFun(a[1], b[1])); } pure T isqrt(T)(T n) { static if (is(T == int)) auto max = 46341; else static if (is(T == long)) auto max = 3037000500L; return iota(T(0), max).lowerBoundBy!("a^^2", "a<=b")(n).back; } pure T icbrt(T)(T n) { static if (is(T == int)) auto max = 1291; else static if (is(T == long)) auto max = 2097152L; return iota(T(0), max).lowerBoundBy!("a^^3", "a<=b")(n).back; } pure T powr(alias pred = "a*b", T, U)(T a, U n, T one) { import std.functional; alias predFun = binaryFun!pred; if (n == 0) return one; auto r = one; for (; n > 0; n >>= 1) { if (n&1) r = predFun(r, a); a = predFun(a, a); } return r; } pure T powr(alias pred = "a*b", T, U)(T a, U n) { return powr!(pred, T, U)(a, n, T(1)); } pure T extGcd(T)(T a, T b, out T x, out T y) { auto g = a; x = 1; y = 0; if (b) { g = extGcd(b, a%b, y, x); y -= a/b*x; } return g; } template MatrixElement(T, alias zero = 0, alias one = 1) { struct Vector { size_t n; @property T[] array() { return a; } alias array this; this(size_t n) in { assert(n > 0); } do { this.n = n; a = new T[](n); static if (T.init != zero) a[] = zero; } this(U)(U[] b) in { assert(b.length > 0); } do { n = b.length; static if (is(T == U)) a = b; else { a = new T[](n); foreach (i; 0..n) a[i] = b[i]; } } pure Vector dup() { auto b = Vector(n); b[] = a[]; return b; } pure Vector opBinary(string op)(Vector b) if (op=="+"||op=="-") in { assert(n == b.n); } do { auto x = Vector(n); foreach (i; 0..n) x[i] = mixin("a[i]"~op~"b[i]"); return x; } ref Vector opOpAssign(string op)(Vector b) if (op=="+"||op=="-") in { assert(n == b.n); } do { foreach (i; 0..n) mixin("a[i]"~op~"=b[i];"); return this; } pure Vector opBinary(string op: "*")(T b) { auto x = Vector(n); foreach (i; 0..n) x[i] = a[i]*b; return x; } ref Vector opOpAssign(string op: "*")(T b) { foreach (i; 0..n) a[i] *= b; return this; } pure T opBinary(string op: "*")(Vector b) in { assert(n == b.n); } do { auto x = zero; foreach (i; 0..n) x += a[i]*b[i]; return x; } private T[] a; } pure T hypot2(Vector a) { return a*a; } pure Vector cross(Vector a, Vector b) in { assert(a.n == 3 && b.n == 3); } do { return Vector([a[1]*b[2]-a[2]*b[1], a[2]*b[0]-a[0]*b[2], a[0]*b[1]-a[1]*b[0]]); } struct Matrix { size_t r, c; @property T[][] array() { return a; } alias array this; static Matrix unit(size_t n) in { assert(n > 0); } do { auto r = Matrix(n, n); foreach (i; 0..n) r[i][i] = one; return r; } this(size_t r, size_t c) in { assert(r > 0 && c > 0); } do { this.r = r; this.c = c; a = new T[][](r, c); static if (T.init != zero) foreach (i; 0..r) a[i][] = zero; } this(U)(U[][] b) 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; 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]; } } pure Matrix dup() { auto b = Matrix(r, c); foreach (i; 0..r) b[i][] = a[i][]; return b; } pure bool opEquals(Matrix b) { return r == b.r && c == b.c && zip(a, b.a).all!"a[0]==a[1]"; } pure Matrix opBinary(string op)(Matrix b) if (op=="+"||op=="-") in { assert(r == b.r && c == b.c); } do { auto x = Matrix(r, c); foreach (i; 0..r) foreach (j; 0..c) x[i][j] = mixin("a[i][j]"~op~"b[i][j]"); return x; } ref Matrix opOpAssign(string op)(Matrix 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[i][j];"); return this; } pure Matrix opBinary(string op: "*")(T b) { auto x = Matrix(r, c); foreach (i; 0..r) foreach (j; 0..c) x[i][j] = a[i][j]*b; return x; } ref Matrix opOpAssign(string op: "*")(T b) { foreach (i; 0..r) foreach (j; 0..c) a[i][j] *= b; return this; } pure Matrix opBinary(string op: "*")(Matrix b) in { assert(c == b.r); } do { auto x = Matrix(r, b.c); foreach (i; 0..r) foreach (j; 0..b.c) foreach (k; 0..c) x[i][j] += a[i][k]*b[k][j]; return x; } ref Matrix opOpAssign(string op: "*")(Matrix b) in { assert(c == b.r); } do { auto x = this*b; r = x.r; c = x.c; a = x.a; return this; } pure Vector opBinary(string op: "*")(Vector b) in { assert(c == b.n); } do { auto x = Vector(r); foreach (i; 0..r) foreach (j; 0..c) x[i] += a[i][j]*b[j]; return x; } pure Matrix opBinary(string op: "^^", U)(U n) in { assert(r == c); } do { return powr(this, n, Matrix.unit(r)); } private T[][] a; } pure T det(Matrix a) in { assert(a.r == a.c); } do { auto n = a.r, b = a.dup, d = 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.conv, std.format, std.meta, std.traits, core.stdc.stdlib; auto getV(T...)(ref T v) { foreach (ref w; v) get(w); } auto getA(T)(size_t n, ref T v) if (hasAssignableElements!T) { v = new T(n); foreach (ref w; v) get(w); } auto 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]); } auto 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...) { auto 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 = " "; } auto put(alias conf = "{}", T...)(T v) { mixin("const PutConf c = "~conf~"; putMain!c(v);"); } auto putB(alias conf = "{}", S, T)(bool c, S t, T f) { if (c) put!conf(t); else put!conf(f); } auto 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; } auto get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); } auto putMain(PutConf c, T...)(T v) { foreach (i, w; v) { putOne!c(w); if (i < v.length-1) OUT.write(c.delimiter); } static if (c.newline) OUT.writeln; static if (c.flush) OUT.flush(); static if (c.exit) exit(0); } auto 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); } auto 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); } } } }