B. Modular Equations
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.
In the only line of the input two space-separated integers a and b (0 ≤ a, b ≤ 109)
are given.
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 .
21 5
2
9435152 272
282
10 10
infinity
In the first sample the answers of the Modular Equation are 8 and 16 since
这题的题意是求(n-m)比m大的因数个数,如果直接求会超时,所以可以用循环从1到i*i<=n-m;然后判断当前i和(n-m)/i是否大于m.
#include<stdio.h>
#include<string.h>
int main()
{
int n,m,i,j,num,t;
while(scanf("%d%d",&n,&m)!=EOF)
{
if(n==m){
printf("infinity\n");continue;
}
num=0;
for(i=1;i*i<=n-m;i++){
if((n-m)%i==0){
t=(n-m)/i;
if(t>m)num++;
if(i>m && i!=t)num++;
}
}
printf("%d\n",num);
}
}
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