// output of ./demo/comb/partition-dist-lex-rec-demo.cc:
// Description:
//% Integer partitions into distinct parts in lexicographic order, recursive algorithm.
//% Cf. OEIS sequence A000009.

arg 1: 19 == n  [Partitions of n]  default=19
arg 2: 0 == mp  [Minimal part > mp,  0 <= mp < n]  default=0
   1:  1 + 2 + 3 + 4 + 9
   2:  1 + 2 + 3 + 5 + 8
   3:  1 + 2 + 3 + 6 + 7
   4:  1 + 2 + 3 + 13
   5:  1 + 2 + 4 + 5 + 7
   6:  1 + 2 + 4 + 12
   7:  1 + 2 + 5 + 11
   8:  1 + 2 + 6 + 10
   9:  1 + 2 + 7 + 9
  10:  1 + 2 + 16
  11:  1 + 3 + 4 + 5 + 6
  12:  1 + 3 + 4 + 11
  13:  1 + 3 + 5 + 10
  14:  1 + 3 + 6 + 9
  15:  1 + 3 + 7 + 8
  16:  1 + 3 + 15
  17:  1 + 4 + 5 + 9
  18:  1 + 4 + 6 + 8
  19:  1 + 4 + 14
  20:  1 + 5 + 6 + 7
  21:  1 + 5 + 13
  22:  1 + 6 + 12
  23:  1 + 7 + 11
  24:  1 + 8 + 10
  25:  1 + 18
  26:  2 + 3 + 4 + 10
  27:  2 + 3 + 5 + 9
  28:  2 + 3 + 6 + 8
  29:  2 + 3 + 14
  30:  2 + 4 + 5 + 8
  31:  2 + 4 + 6 + 7
  32:  2 + 4 + 13
  33:  2 + 5 + 12
  34:  2 + 6 + 11
  35:  2 + 7 + 10
  36:  2 + 8 + 9
  37:  2 + 17
  38:  3 + 4 + 5 + 7
  39:  3 + 4 + 12
  40:  3 + 5 + 11
  41:  3 + 6 + 10
  42:  3 + 7 + 9
  43:  3 + 16
  44:  4 + 5 + 10
  45:  4 + 6 + 9
  46:  4 + 7 + 8
  47:  4 + 15
  48:  5 + 6 + 8
  49:  5 + 14
  50:  6 + 13
  51:  7 + 12
  52:  8 + 11
  53:  9 + 10
  54:  19
 19:  ct=54