m2a = ->m {
  c = [[[[]]]]
  (1..m).each_with_object([]) {|s, a|
    (1..s).each {|w|
      (1..[s, 5].min).each {|hd|
        c[s - hd][w - 1]&.each {|tl|
          b = [hd, tl]
          (a[s] ||= [nil]) << b
          ((c[s] ||= [])[w] ||= []) << b
        }
      }
    }
  }
}
a = m2a.(20)
g = ->m, n {puts "(#{m},#{n}) → #{(a[m][n] || [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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