Our aim is to split a fraction into a number of elements is a denominator is a positive integer fraction of the sum of form. For example, 2/3 can be split into 1/2+1/6 form. Not considered here, the order, such as 1/6+1/2 and 1/2+1/6 of the same. Input p, q, a, n, where p/q as a fraction of this split scores require no more than the number of split points n-all the product of the denominator can not be larger than a. How many kinds of demand split method? Input: Up to 200 sets of data. In each line has four numbers indicate the p, q, a, n, separated by a space between, and meet the p, q < = 800, a < = 12000, n < = 7, the end, four 0 as the input end. Input Example: 2,312,032,330,030,000 sample output: 47

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