Masha and geometric depression

1000ms

262144K

Description:

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 b_i = b_i - 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, ..., a_m, and an integer l.

Masha writes all progression terms one by one onto the board (including repetitive) while condition |b_i| ≤ 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.

Input:

The first line of input contains four integers b₁, q, l, m (-10⁹ ≤ b₁, q ≤ 10⁹, 1 ≤ l ≤ 10⁹, 1 ≤ m ≤ 10⁵) — the initial term and the common ratio of progression, absolute value of maximal number that can be written on the board and the number of "bad" integers, respectively.

The second line contains m distinct integers a₁, a₂, ..., a_m (-10⁹ ≤ a_i ≤ 10⁹) — numbers that will never be written on the board.

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.

Sample Input:

3 2 30 4
6 14 25 48

Sample Output:

Sample Input:

123 1 2143435 4
123 11 -5453 141245

Sample Output:

Sample Input:

123 1 2143435 4
54343 -13 6 124

Sample Output:

inf

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.

Informação

Provedor Codeforces

Código CF789B