CF789B Masha and geometric depression

Masha really loves algebra. On the last lesson, her strict teacher Dvastan gave she new exercise. You are given geometric progression $ b $ defined by two integers $ b_{1} $ and $ q $ . Remind that a geometric progression is a sequence of integers $ b_{1},b_{2},b_{3},... $ , where for each $ i>1 $ the respective term satisfies the condition $ b_{i}=b_{i-1}·q $ , where $ q $ is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both $ b_{1} $ and $ q $ can equal $ 0 $ . Also, Dvastan gave Masha $ m $ "bad" integers $ a_{1},a_{2},...,a_{m} $ , and an integer $ l $ . Masha writes all progression terms one by one onto the board (including repetitive) while condition $ |b_{i}|

The first line of input contains four integers $ b_{1} $ , $ q $ , $ l $ , $ m $ (- $ 10^{9}

Print the only integer, meaning the number of progression terms that will be written on the board if it is finite, or "inf" (without quotes) otherwise.

In the first sample case, Masha will write integers $ 3,12,24 $ . Progression term $ 6 $ will be skipped because it is a "bad" integer. Terms bigger than $ 24 $ won't be written because they exceed $ l $ by absolute value. In the second case, Masha won't write any number because all terms are equal $ 123 $ and this is a "bad" integer. In the third case, Masha will write infinitely integers $ 123 $ .