def solve(io) a, b = io.get2 pf = PrimeFactor.sqrt(a+b) pf.divisors(a+b).each do |c| io.put_e c if a != c && b != c && (a+c)%b == 0 && (b+c)%a == 0 end io.put -1 end struct Int def cdiv(b : Int) (self + b - 1) // b end def bit?(i : Int) bit(i) == 1 end def set_bit(i : Int) self | (self.class.new(1) << i) end def reset_bit(i : Int) self & ~(self.class.new(1) << i) end {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.34.0") < 0 %} def bit_length : Int32 x = self < 0 ? ~self : self if x.is_a?(Int::Primitive) Int32.new(sizeof(self) * 8 - x.leading_zeros_count) else to_s(2).size end end {% end %} end struct Int32 SQRT_MAX = 46_340_i32 def isqrt m = SQRT_MAX r = (1_i32..SQRT_MAX).bsearch { |i| i**2 > self } r.nil? ? SQRT_MAX : r - 1 end end struct Int64 SQRT_MAX = 3_037_000_499_i64 def isqrt r = (1_i64..SQRT_MAX).bsearch { |i| i**2 > self } r.nil? ? SQRT_MAX : r - 1 end end struct Number {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "1.1.0") < 0 %} def zero? self == 0 end def positive? self > 0 end def negative? self < 0 end {% end %} {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.36.0") < 0 %} def self.additive_identity zero end def self.multiplicative_identity new(1) end {% end %} end class Array macro new_md(*args, &block) {% if !block %} {% for arg, i in args[0...-2] %} Array.new({{arg}}) { {% end %} Array.new({{args[-2]}}, {{args[-1]}}) {% for arg in args[0...-2] %} } {% end %} {% else %} {% for arg, i in args %} Array.new({{arg}}) { |_i{{i}}| {% end %} {% for block_arg, i in block.args %} {{block_arg}} = _i{{i}} {% end %} {{block.body}} {% for arg in args %} } {% end %} {% end %} end end class ProconIO def initialize(@ins : IO = STDIN, @outs : IO = STDOUT) @buf = [] of String @index = 0 end def get(k : T.class = Int32) forall T get_v(k) end macro define_get {% for i in (2..9) %} def get( {% for j in (1..i) %} k{{j}}{% if j < i %},{% end %} {% end %} ) { {% for j in (1..i) %} get(k{{j}}){% if j < i %},{% end %} {% end %} } end {% end %} end define_get macro define_getn {% for i in (2..9) %} def get{{i}}(k : T.class = Int32) forall T get( {% for j in (1..i) %} k{% if j < i %}, {% end %} {% end %} ) end {% end %} end define_getn def get_a(n : Int, k : T.class = Int32) forall T Array.new(n) { get_v(k) } end def get_c(n : Int, k : T.class = Int32) forall T get_a(n, k) end macro define_get_c {% for i in (2..9) %} def get_c( n : Int, {% for j in (1..i) %} k{{j}}{% if j < i %},{% end %} {% end %} ) a = Array.new(n) do get( {% for j in (1..i) %} k{{j}}{% if j < i %},{% end %} {% end %} ) end { {% for j in (1..i) %} a.map { |e| e[{{j-1}}] }{% if j < i %},{% end %} {% end %} } end {% end %} end define_get_c macro define_getn_c {% for i in (2..9) %} def get{{i}}_c(n : Int, k : T.class = Int32) forall T get_c( n, {% for j in (1..i) %} k{% if j < i %}, {% end %} {% end %} ) end {% end %} end define_getn_c def get_m(r : Int, c : Int, k : T.class = Int32) forall T Array.new(r) { get_a(c, k) } end def put(*vs) vs.each.with_index do |v, i| put_v(v) @outs.print i < vs.size - 1 ? " " : "\n" end end def put_e(*vs) put(*vs) exit end private def get_v(k : Int32.class); get_token.to_i32; end private def get_v(k : Int64.class); get_token.to_i64; end private def get_v(k : UInt32.class); get_token.to_u32; end private def get_v(k : UInt64.class); get_token.to_u64; end private def get_v(k : Float64.class); get_token.to_f64; end private def get_v(k : String.class); get_token; end private def get_token if @buf.size == @index str = @ins.read_line @buf = str.split @index = 0 end v = @buf[@index] @index += 1 v end private def put_v(vs : Enumerable) vs.each_with_index do |v, i| @outs.print v @outs.print " " if i < vs.size - 1 end end private def put_v(v) @outs.print v end end macro min_u(a, b) {{a}} = Math.min({{a}}, {{b}}) end macro max_u(a, b) {{a}} = Math.max({{a}}, {{b}}) end macro zip(a, *b, &block) {{a}}.zip({{*b}}) {{block}} end require "bit_array" def powr(a : T, n : Int, i : T = T.multiplicative_identity) forall T powr(a, n, i) { |a, b| a * b } end def powr(a : T, n : Int, i : T = T.multiplicative_identity, &block) forall T return i if n == 0 r, b = i, a while n > 0 r = yield r, b if n.bit(0) == 1 b = yield b, b n >>= 1 end r end def ext_gcd(a : T, b : T) forall T if a == 0 {b, T.new(0), T.new(1)} else g, x, y = ext_gcd(b%a, a) {g, y-(b//a)*x, x} end end class PrimeFactor def initialize(@n : Int32) s = (@n+1)//2 sieve = BitArray.new(s, true) if @n < 2 @primes = [] of Int32 return end (1..(n.isqrt-1)//2).each do |p| if sieve[p] (p*3+1...s).step(p*2+1) do |q| sieve[q] = false end end end @primes = [2] (1...s).each do |p| @primes << p*2+1 if sieve[p] end end def self.sqrt(n : Int) self.new(n.isqrt.to_i32) end getter primes : Array(Int32) record Factor(T), prime : T, exp : Int32 def div(x : T) forall T factors = [] of Factor(T) t = x.isqrt @primes.each do |p| break if p > t c = 0 while x%p == 0 c += 1 x //= p end factors << Factor.new(T.new(p), c) if c > 0 break if x == 1 end factors << Factor.new(x, 1) if x > 1 factors end def divisors(x : T) forall T factors = div(x) r = divisors_proc(factors, 0, T.multiplicative_identity) r.sort! end def divisors_proc(factors : Array(Factor(T)), i : Int32, c : T) forall T return [c] if i == factors.size r = [] of T (0..factors[i].exp).each do |j| r.concat(divisors_proc(factors, i+1, c * factors[i].prime**j)) end r end end solve(ProconIO.new)