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 b1 and q. Remind that a geometric progression is a sequence of integers b1,b2,b3,..., where for each i>1 the respective term satisfies the condition bi=bi-1·q, where q is called the common ratio of the progression. Progressions in Uzhlyandia are unusual: both b1 and q can equal 0. Also, Dvastan gave Masha m "bad" integers a1,a2,...,am, and an integer l.
Masha writes all progression terms one by one onto the board (including repetitive) while condition |bi|≤l is satisfied (|x| means absolute value of x). There is an exception: if a term equals one of the "bad" integers, Masha skips it (doesn't write onto the board) and moves forward to the next term.
But the lesson is going to end soon, so Masha has to calculate how many integers will be written on the board. In order not to get into depression, Masha asked you for help: help her calculate how many numbers she will write, or print "inf" in case she needs to write infinitely many integers.
Output
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.
Note
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.