5405: Vasya and Polynomial
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
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提交：3
通过：1
题目描述
Vasya is studying in the last class of school and soon he will take exams. He decided to study polynomials. Polynomial is a function P(x)=a0+a1x1+...+anxn. Numbers ai are called coefficients of a polynomial, non-negative integer n is called a degree of a polynomial.
Vasya has made a bet with his friends that he can solve any problem with polynomials. They suggested him the problem: "Determine how many polynomials P(x) exist with integer non-negative coefficients so that
, and 
, where 
and b are given positive integers"?
Vasya does not like losing bets, but he has no idea how to solve this task, so please help him to solve the problem.
Vasya has made a bet with his friends that he can solve any problem with polynomials. They suggested him the problem: "Determine how many polynomials P(x) exist with integer non-negative coefficients so that
, and , where and b are given positive integers"?
Vasya does not like losing bets, but he has no idea how to solve this task, so please help him to solve the problem.
Input
The input contains three integer positive numbers 
no greater than 1018.
Output
If there is an infinite number of such polynomials, then print "inf" without quotes, otherwise print the reminder of an answer modulo 109+7.
Examples
Input
2 2 2
Output
2
Input
2 3 3
Output
1
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