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) = 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.

输入描述:

The input contains three integer positive numbers no greater than 1018.

输出描述:

If there is an infinite number of such polynomials, then print "inf" without quotes, otherwise print the reminder of an answer modulo 109 + 7.