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.


function countcoins(t, o) {
    'use strict';
    var targetsLength = t + 1;
    var operandsLength = o.length;
    t = [1];
 
    for (var a = 0; a < operandsLength; a++) {
        for (var b = 1; b < targetsLength; b++) {
 
            // initialise undefined target
            t[b] = t[b] ? t[b] : 0;
 
            // accumulate target + operand ways
            t[b] += (b < o[a]) ? 0 : t[b - o[a]];
        }
    }
 
    return t[targetsLength - 1];
}