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.


def ccR
ccR = { BigInteger tot, List<BigInteger> coins ->
    BigInteger n = coins.size()
    switch ([tot:tot, coins:coins]) {
        case { it.tot == 0 } :
            return 1g
        case { it.tot < 0 || coins == [] } :
            return 0g
        default:
            return ccR(tot, coins[1..<n]) +
                ccR(tot - coins[0], coins)
    }
}