|시간 제한||메모리 제한||제출||정답||맞은 사람||정답 비율|
|1 초||128 MB||3||3||3||100.000%|
Let’s play a stone removing game.
Initially, n stones are arranged on a circle and numbered 1, . . . , n clockwise (Figure 1). You are also given two numbers k and m. From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone m. In step 2, locate the k-th next stone clockwise from m and remove it. In subsequent steps, start from the slot of the stone removed in the last step, make k hops clockwise on the remaining stones and remove the one you reach. In other words, skip (k − 1) remaining stones clockwise and remove the next one. Repeat this until only one stone is left and answer its number.
For example, the answer for the case n = 8, k = 5, m = 3 is 1, as shown in Figure 1.
Figure 1: An example game
The input consists of multiple datasets each of which is formatted as follows.
n k m
The last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.
2≤n≤10000, 1≤k≤10000, 1≤m≤n
The number of datasets is less than 100.
For each dataset, output a line containing the stone number left in the final state. No extra characters such as spaces should appear in the output.
8 5 3 100 9999 98 10000 10000 10000 0 0 0
1 93 2019