// output of ./demo/comb/composition-nz-max-demo.cc:
// Description:
//% Compositions of n into positive parts <= mx.
//% Lexicographic order.

arg 1: 9 == n  [compositions of n into parts <= mx]  default=9
arg 2: 2 == mx  [parts <= mx (mx>=1)]  default=2
   1:  [ 9]  .........  [ 1 1 1 1 1 1 1 1 1 ]
   2:  [ 8]  ........1  [ 1 1 1 1 1 1 1 2 ]
   3:  [ 8]  .......1.  [ 1 1 1 1 1 1 2 1 ]
   4:  [ 8]  ......1..  [ 1 1 1 1 1 2 1 1 ]
   5:  [ 7]  ......1.1  [ 1 1 1 1 1 2 2 ]
   6:  [ 8]  .....1...  [ 1 1 1 1 2 1 1 1 ]
   7:  [ 7]  .....1..1  [ 1 1 1 1 2 1 2 ]
   8:  [ 7]  .....1.1.  [ 1 1 1 1 2 2 1 ]
   9:  [ 8]  ....1....  [ 1 1 1 2 1 1 1 1 ]
  10:  [ 7]  ....1...1  [ 1 1 1 2 1 1 2 ]
  11:  [ 7]  ....1..1.  [ 1 1 1 2 1 2 1 ]
  12:  [ 7]  ....1.1..  [ 1 1 1 2 2 1 1 ]
  13:  [ 6]  ....1.1.1  [ 1 1 1 2 2 2 ]
  14:  [ 8]  ...1.....  [ 1 1 2 1 1 1 1 1 ]
  15:  [ 7]  ...1....1  [ 1 1 2 1 1 1 2 ]
  16:  [ 7]  ...1...1.  [ 1 1 2 1 1 2 1 ]
  17:  [ 7]  ...1..1..  [ 1 1 2 1 2 1 1 ]
  18:  [ 6]  ...1..1.1  [ 1 1 2 1 2 2 ]
  19:  [ 7]  ...1.1...  [ 1 1 2 2 1 1 1 ]
  20:  [ 6]  ...1.1..1  [ 1 1 2 2 1 2 ]
  21:  [ 6]  ...1.1.1.  [ 1 1 2 2 2 1 ]
  22:  [ 8]  ..1......  [ 1 2 1 1 1 1 1 1 ]
  23:  [ 7]  ..1.....1  [ 1 2 1 1 1 1 2 ]
  24:  [ 7]  ..1....1.  [ 1 2 1 1 1 2 1 ]
  25:  [ 7]  ..1...1..  [ 1 2 1 1 2 1 1 ]
  26:  [ 6]  ..1...1.1  [ 1 2 1 1 2 2 ]
  27:  [ 7]  ..1..1...  [ 1 2 1 2 1 1 1 ]
  28:  [ 6]  ..1..1..1  [ 1 2 1 2 1 2 ]
  29:  [ 6]  ..1..1.1.  [ 1 2 1 2 2 1 ]
  30:  [ 7]  ..1.1....  [ 1 2 2 1 1 1 1 ]
  31:  [ 6]  ..1.1...1  [ 1 2 2 1 1 2 ]
  32:  [ 6]  ..1.1..1.  [ 1 2 2 1 2 1 ]
  33:  [ 6]  ..1.1.1..  [ 1 2 2 2 1 1 ]
  34:  [ 5]  ..1.1.1.1  [ 1 2 2 2 2 ]
  35:  [ 8]  .1.......  [ 2 1 1 1 1 1 1 1 ]
  36:  [ 7]  .1......1  [ 2 1 1 1 1 1 2 ]
  37:  [ 7]  .1.....1.  [ 2 1 1 1 1 2 1 ]
  38:  [ 7]  .1....1..  [ 2 1 1 1 2 1 1 ]
  39:  [ 6]  .1....1.1  [ 2 1 1 1 2 2 ]
  40:  [ 7]  .1...1...  [ 2 1 1 2 1 1 1 ]
  41:  [ 6]  .1...1..1  [ 2 1 1 2 1 2 ]
  42:  [ 6]  .1...1.1.  [ 2 1 1 2 2 1 ]
  43:  [ 7]  .1..1....  [ 2 1 2 1 1 1 1 ]
  44:  [ 6]  .1..1...1  [ 2 1 2 1 1 2 ]
  45:  [ 6]  .1..1..1.  [ 2 1 2 1 2 1 ]
  46:  [ 6]  .1..1.1..  [ 2 1 2 2 1 1 ]
  47:  [ 5]  .1..1.1.1  [ 2 1 2 2 2 ]
  48:  [ 7]  .1.1.....  [ 2 2 1 1 1 1 1 ]
  49:  [ 6]  .1.1....1  [ 2 2 1 1 1 2 ]
  50:  [ 6]  .1.1...1.  [ 2 2 1 1 2 1 ]
  51:  [ 6]  .1.1..1..  [ 2 2 1 2 1 1 ]
  52:  [ 5]  .1.1..1.1  [ 2 2 1 2 2 ]
  53:  [ 6]  .1.1.1...  [ 2 2 2 1 1 1 ]
  54:  [ 5]  .1.1.1..1  [ 2 2 2 1 2 ]
  55:  [ 5]  .1.1.1.1.  [ 2 2 2 2 1 ]
 ct=55