There are four types of common coins in   US   currency:

   quarters   (25 cents)
   dimes   (10 cents)
   nickels   (5 cents),   and 
   pennies   (1 cent) 


There are six ways to make change for 15 cents:

   A dime and a nickel 
   A dime and 5 pennies
   3 nickels
   2 nickels and 5 pennies
   A nickel and 10 pennies
   15 pennies


Task

How many ways are there to make change for a dollar using these common coins?     (1 dollar = 100 cents).



Optional

Less common are dollar coins (100 cents);   and very rare are half dollars (50 cents).   With the addition of these two coins, how many ways are there to make change for $1000?

(Note:   the answer is larger than   232).



References

 an algorithm from the book Structure and Interpretation of Computer Programs.
 an article in the algorithmist.
 Change-making problem on Wikipedia.


  [ stack ]                      is lim        (     --> s )
 
  [ swap dup 1+ lim put
    1 0 rot of join
    swap witheach
      [ 0 over of
        swap negate temp put
        lim share times
          [ over i^ peek
            over temp share peek
            + join ]
        temp take negate split
        nip nip ]
    -1 peek
    lim release ]                is makechange ( n [ --> n )
 
  say "With US coins." cr
  100 ' [ 1 5 10 25 ] makechange echo cr
  100000 ' [ 1 5 10 25 50 100 ] makechange echo cr
  cr
  say "With EU coins." cr
  100 ' [ 1 2 5 10 20 50 100 200 ] makechange echo cr
  100000 ' [ 1 2 5 10 20 50 100 200 ] makechange echo cr