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Flavius Josephus Reloaded
Flavius Josephus once was trapped in a cave together with his comrade soldiers surrounded by Romans. All of Josephus’ fellow soldiers preferred not to surrender but to commit suicide. So they all formed a circle and agreed on a number k. Every k-th person in the circle would then commit suicide. However, Josephus had different priorities and didn’t want to die just yet. According to the legend he managed to find the safe spot in the circle where he would be the last one to commit suicide. He surrendered to the Romans and became a citizen of Rome a few years later.
It is a lesser known fact that the souls of Josephus and his comrades were all born again in modern times. Obviously Josephus and his reborn fellow soldiers wanted to avoid a similar fiasco in the future. Thus they asked a consulting company to work out a better decision scheme. The company came up with the following scheme:
You are to write a program that given the number of soldiers N and the constants a and b determines the number of survivors.
The input file consists of several test cases. Each test case consists of a single line containing the three integers N (2 ≤ N ≤ 109), a and b (0 ≤ a, b < N) separated by white space. You may safely assume that the first soldier dies after no more than one million (106) steps. The input is terminated by a single number 0 which should not be processed.
For each test case output a single line containing the number of soldiers that survive.
2 1 1 5 1 1 10 3 7 101 9 2 698253463 1 181945480 1000000000 999999999 999999999 0
0 2 4 96 698177783 999999994
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