time limit per test

memory limit per test

input

output

Last week, Hamed learned about a new type of equations in his math class called Modular Equations. Lets define i modulo j as the remainder of division of i by j and denote it by . A Modular Equation, as Hamed's teacher described, is an equation of the form in which a and b are two non-negative integers and x is a variable. We call a positive integer x for which asolution of our equation.

Hamed didn't pay much attention to the class since he was watching a movie. He only managed to understand the definitions of these equations.

Now he wants to write his math exercises but since he has no idea how to do that, he asked you for help. He has told you all he knows about Modular Equations and asked you to write a program which given two numbers a and b determines how many answers the Modular Equation has.

Input

In the only line of the input two space-separated integers a and b (0?≤?a,?b?≤?109) are given.

Output

If there is an infinite number of answers to our equation, print "infinity" (without the quotes). Otherwise print the number of solutions of the Modular Equation .

Sample test(s)

input

21 5

output

input

9435152 272

output

282

input

10 10

output

infinity

Note

In the first sample the answers of the Modular Equation are 8 and 16 since

題意：給出a，b，問有多少滿足a % x == b的正整數x存在。

分析：暴力可解。a % x == b有(a - b) % x == 0，也就是找a - b的因子。前提是：x是正整數，但是要注意需滿足x > b（余數比除數小），當a < b時，此時沒有x滿足條件，輸出0即可；當a == b時，應輸出“infinity”；否則的話，直接暴力找a - b的因子即可。

AC代碼：

#include #include #include #include #include #include #include #include 

Python版：

a, b = map(int, raw_input().split())if a == b: print 'infinity'elif a < b: print 0else: a -= b i = 1 ans = 0 while i*i <= a: if a % i == 0: if i > b: ans += 1 if a/i > b and i*i != a: ans += 1 i += 1 print ans

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