f433:
165 - Stamps

Content

給H,K詢問有K種面額且用H張郵票最大能由1連續表示到多少(H+K<=9)

The government of Nova Mareterrania requires that various legal documents have stamps attached to them so that the government can derive revenue from them. In terms of recent legislation, each class of document is limited in the number of stamps that may be attached to it. The government wishes to know how many different stamps, and of what values, they need to print to allow the widest choice of values to be made up under these conditions. Stamps are always valued in units of 1.

This has been analysed by government mathematicians who have derived a formula for n(h, k), where h is the number of stamps that may be attached to a document, k is the number of denominations of stamps available, and n is the largest attainable value in a continuous sequence starting from 1. For instance, if h = 3, k = 2 and the denominations are 1 and 4, we can make all the values from 1 to 6 (as well as 8, 9 and 12). However with the same values of h and k, but using 1 and 3 stamps we can make all the values from 1 to 7 (as well as 9). This is maximal, so n(3, 2) = 7.

Unfortunately the formula relating n(h, k) to h, k and the values of the stamps has been lost — it was published in one of the government reports but no-one can remember which one, and of the three researchers who started to search for the formula, two died of boredom and the third took a job as a lighthouse keeper because it provided more social stimulation.

The task has now been passed on to you. You doubt the existence of a formula in the first place so you decide to write a program that, for given values of h and k, will determine an optimum set of stamps and the value of n(h, k).

Input

每一行分別是H和K

H和K皆為0時結束

Output

輸出面額和最大能表示到多少

面額和最大值之間輸出"->"

Sample Input
#1

3 2 0 0

Sample Output
#1

1 3 -> 7

測資資訊：

記憶體限制：
512
MB

公開 測資點#0 (100%): 1.0s , <1K

公開 測資點#0 (100%): 1.0s , <1K

用1 3能表示

1：1 2：1,1 3：3 4：1,3 5：1,1,3 6：3,3 7：1,1,3

且7已經是能連續表示的最大值了

2020 10月CPE第七題

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