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E. Vasya and Polynomial

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya 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*) = *a*_{0} + *a*_{1}*x*^{1} + ... + *a*_{n}*x*^{n}. Numbers *a*_{i} 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.

Input

The input contains three integer positive numbers no greater than 10^{18}.

Output

If there is an infinite number of such polynomials, then print "inf" without quotes, otherwise print the reminder of an answer modulo 10^{9} + 7.

Examples

Input

2 2 2

Output

2

Input

2 3 3

Output

1

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