def solve(io) n, k = io.get2 g = n.gcd(k) pf = PrimeFactor.sqrt(g) ft = Fact(Mint).new(n) a = Hash(Int32, Mint).new(Mint.zero) pf.divisors(g).reverse_each do |di| next if di == 1 i = n // di a[i] = ft.combi(i, k // di) pf.divisors(i).each do |ei| next if ei == i a[i] -= a[ei] end end io.put a.values.sum end class ProconIO def initialize(@ins : IO = STDIN, @outs : IO = STDOUT) @buf = IO::Memory.new("") end def get(k : T.class = Int32) forall T get_v(k) end macro define_get {% for i in (2..9) %} def get({{ *(1..i).map { |j| "k#{j}".id } }}) { {{ *(1..i).map { |j| "get(k#{j})".id } }} } end {% end %} end define_get macro define_getn {% for i in (2..9) %} def get{{i}}(k : T.class = Int32) forall T get({{ *(1..i).map { "k".id } }}) 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, {{ *(1..i).map { |j| "k#{j}".id } }}) a = Array.new(n) { get({{ *(1..i).map { |j| "k#{j}".id } }}) } { {{ *(1..i).map { |j| "a.map { |e| e[#{j-1}] }".id } }} } 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, {{ *(1..i).map { "k".id } }}) 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 macro define_put {% for i in (1..9) %} def put({{ *(1..i).map { |j| "v#{j}".id } }}, *, delimiter = " ") {% for j in (1..i) %} print_v(v{{j}}, delimiter) {% if j < i %}@outs << delimiter{% end %} {% end %} @outs.puts end {% end %} end define_put def put_e(*vs) put(*vs) exit end def put_f(*vs) put(*vs) @outs.flush 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 loop do token = @buf.gets(' ', chomp: true) break token unless token.nil? @buf = IO::Memory.new(@ins.read_line) end end private def print_v(v, dlimiter) @outs << v end private def print_v(v : Enumerable, delimiter) v.each_with_index do |e, i| @outs << e @outs << delimiter if i < v.size - 1 end end 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", "0.35.0") < 0 %} def digits(base = 10) raise ArgumentError.new("Invalid base #{base}") if base < 2 raise ArgumentError.new("Can't request digits of negative number") if self < 0 return [0] if self == 0 num = self digits_count = (Math.log(self.to_f + 1) / Math.log(base)).ceil.to_i ary = Array(Int32).new(digits_count) while num != 0 ary << num.remainder(base).to_i num = num.tdiv(base) end ary end {% 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 Float64 def near?(x) (self - x).abs <= (self.abs < x.abs ? x.abs : self.abs) * EPSILON 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 module Math {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "1.2.0") < 0 %} def isqrt(value : Int::Primitive) raise ArgumentError.new "Input must be non-negative integer" if value < 0 return value if value < 2 res = value.class.zero bit = res.succ << (res.leading_zeros_count - 2) bit >>= value.leading_zeros_count & ~0x3 while (bit != 0) if value >= res + bit value -= res + bit res = (res >> 1) + bit else res >>= 1 end bit >>= 2 end res end {% 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 class PrimeFactor def initialize(@n : Int32) s = (@n + 1) // 2 sieve = Array.new(s, true) if @n < 2 @primes = [] of Int32 return end m = (Math.isqrt(n) - 1) // 2 (1..m).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(Math.isqrt(n).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 = Math.isqrt(x) @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 class Fact(T) def initialize(@n : Int32) @table = Array.new(@n+1, T.multiplicative_identity) (1..@n).each do |i| @table[i] = @table[i-1] * i end @inv_table = Array.new(@n+1, T.multiplicative_identity) @inv_table[@n] //= @table[@n] (1..@n).reverse_each do |i| @inv_table[i-1] = @inv_table[i] * i end end getter table : Array(T) getter inv_table : Array(T) def fact(n : Int) @table[n] end def perm(n : Int, r : Int) @table[n] * @inv_table[n-r] end def combi(n : Int, r : Int) @table[n] * @inv_table[r] * @inv_table[n-r] end def homo(n : Int, r : Int) combi(n + r - 1, r) end @table : Array(T) @inv_table : Array(T) end 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 def bit_subsets(a : Int, includes_zero = false) n = i = a if includes_zero while i >= 0 yield i & n i = (i & n) - 1 end else while i > 0 yield i i = (i - 1) & n end end end def bit_zeta_trans_subset(n : Int, f : Array(T), &compose : (T, T) -> T) forall T g = Array.new(1 << n) { |i| f[i] } n.times do |i| (1 << n).times do |j| if j >> i & 1 != 0 g[j] = compose.call(g[j], g[j ^ (1 << i)]) end end end g end def bit_zeta_trans_superset(n : Int, f : Array(T), &compose : (T, T) -> T) forall T g = Array.new(1 << n) { |i| f[i] } n.times do |i| (1 << n).times do |j| if j >> i & 1 == 0 g[j] = compose.call(g[j], g[j ^ (1 << i)]) end end end g end abstract struct ModInt < Number macro new_type(name, mod) struct {{name}} < ModInt @@mod : Int32 = {{mod}} end end def initialize(v : Int) @v = (v % @@mod).to_i64 end def_hash @@mod, @v def to_s @v.to_s end def to_s(io : IO) : Nil @v.to_s(io) end getter v : Int64 delegate to_i, to: @v def ==(r : self) @v == r.v end def ==(r : Int) @v == (r % @@mod) end def - : self m(-@v) end def +(r : self) m(@v + r.v) end def +(r : Int) self + m(r) end def -(r : self) m(@v - r.v) end def -(r : Int) self - m(r) end def *(r : self) m(@v * r.v) end def *(r : Int) self * m(r) end def //(r : self) self * r.inv end def //(r : Int) self // m(r) end def **(n : Int) powr(self, n) end def inv m(ext_gcd(@v.to_i32, @@mod)[1]) end private def m(v : Int) self.class.new(v) end end ModInt.new_type(Mint, 10**9+7) solve(ProconIO.new)