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Ms. Iyo Kiffa-Australis has a balance and only two kinds of weights to measure a dose of medicine. For example, to measure of aspirin using weights and weights, she can put one weight on the side of the medicine and three weights on the opposite side (Figure 1). Although she could put four weights on the medicine side and two weights on the other (Figure 2), she would not choose this solution because it is less convenient to use more weights.
You are asked to help her by calculating how many weights are required.
The input is a sequence of datasets. A dataset is a line containing three positive integers , , and separated by a space. The following relations hold: , , , and . You may assume that it is possible to measure mg using a combination of mg and mg weights. In other words, you need not consider
no solution cases.
The end of the input is indicated by a line containing three zeros separated by a space. It is not a dataset.
The output should be composed of lines, each corresponding to an input dataset . An output line should contain two nonnegative integers and separated by a space. They should satisfy the following three conditions.
No extra characters (e.g. extra spaces) should appear in the output.
700 300 200 500 200 300 500 200 500 275 110 330 275 110 385 648 375 4002 3 1 10000 0 0 0
1 3 1 1 1 0 0 3 1 1 49 74 3333 1