def gm1(m)
  q, r = m.divmod 5
  (0 < r ? [r] : []) + [5] * q
end
def next_or_nil(a)
  a = a.dup
  k = a.rindex {|ak| 1 < ak}
  i = k && (k-1).downto(0).find {|i| a[i] != 5}
  if !k
    nil
  elsif !i
    a[k] -= 1
    ([1] + a.reverse)
  else
    a[i] += 1
    a[k] -= 1
    a[i+1..-1] = a[i+1..-1].reverse
    a
  end
end
def nexts(a)
  [a].tap {|b| b << a while a = next_or_nil(a)}
end
 
ga = (1..20).map{|m| nexts(gm1(m))}
g = ->m, n {puts "(#{m},#{n}) → #{(ga[m - 1][n - 1] || [0]).join}"}
 
g.(2,1)
g.(2,2)
g.(2,3)
g.(20,1)
g.(20,2)
g.(20,3)
g.(20,400096)
g.(20,400097)
#g.(32,1)
#g.(32,2)
#g.(32,3)
#g.(32,1000)
#g.(32,1000000)
#g.(32,1000000000)
#g.(32,1333610936)
#g.(32,1333610937)
 

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