CF493E.Vasya and Polynomial

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.

瓦西娅正在读高中的最后一年，不久后他将参加考试。他决定学习多项式。多项式是一个函数 $ P(x) = a_0 + a_1 x^1 + \dots + a_n x^n $。其中，数 $ a_i $ 称为该多项式的系数，非负整数 $ n $ 称为该多项式的次数。

瓦西娅和他的朋友们打了个赌，声称自己能解决任何关于多项式的题目。朋友们给他出了一道题：“求满足以下条件的多项式 $ P(x) $ 的个数：其所有系数均为非负整数，且满足
，
以及
，
其中
和 $ b $ 是给定的正整数。”

瓦西娅不喜欢输掉赌注，但他完全不知道如何解决这个问题，因此请帮帮他解决这道题。

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

输入包含三个不超过 $10^{18}$ 的正整数 。

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

如果满足条件的多项式有无穷多个，则输出 inf（不带引号）；否则输出答案对 $10^9 + 7$ 取模后的余数。