CF1928C Physical Education Lesson

In a well-known school, a physical education lesson took place. As usual, everyone was lined up and asked to settle in "the first– $ k $ -th" position. As is known, settling in "the first– $ k $ -th" position occurs as follows: the first $ k $ people have numbers $ 1, 2, 3, \ldots, k $ , the next $ k - 2 $ people have numbers $ k - 1, k - 2, \ldots, 2 $ , the next $ k $ people have numbers $ 1, 2, 3, \ldots, k $ , and so on. Thus, the settling repeats every $ 2k - 2 $ positions. Examples of settling are given in the "Note" section. The boy Vasya constantly forgets everything. For example, he forgot the number $ k $ described above. But he remembers the position he occupied in the line, as well as the number he received during the settling. Help Vasya understand how many natural numbers $ k $ fit under the given constraints. Note that the settling exists if and only if $ k > 1 $ . In particular, this means that the settling does not exist for $ k = 1 $ .

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In the first test case, $ k $ equals $ 2, 3, 5, 6 $ are suitable. An example of settling for these $ k $ : $ k $ / № $ 1 $ $ 2 $ $ 3 $ $ 4 $ $ 5 $ $ 6 $ $ 7 $ $ 8 $ $ 9 $ $ 10 $ $ 2 $ $ 1 $ $ 2 $ $ 1 $ $ 2 $ $ 1 $ $ 2 $ $ 1 $ $ 2 $ $ 1 $ $ 2 $ $ 3 $ $ 1 $ $ 2 $ $ 3 $ $ 2 $ $ 1 $ $ 2 $ $ 3 $ $ 2 $ $ 1 $ $ 2 $ $ 5 $ $ 1 $ $ 2 $ $ 3 $ $ 4 $ $ 5 $ $ 4 $ $ 3 $ $ 2 $ $ 1 $ $ 2 $ $ 6 $ $ 1 $ $ 2 $ $ 3 $ $ 4 $ $ 5 $ $ 6 $ $ 5 $ $ 4 $ $ 3 $ $ 2 $ In the second test case, $ k = 2 $ is suitable.