POJ C Looooops

Description

A Compiler Mystery: We are given a C-language style for loop of type

for (variable = A; variable != B; variable += C)

 statement;

I.e., a loop which starts by setting variable to value A and while variable is not equal to B, repeats statement followed by increasing the variable by C. We want to know how many times does the statement get executed for particular values of A, B and C, assuming
that all arithmetics is calculated in a k-bit unsigned integer type (with values 0 <= x < 2 ^k) modulo 2 ^k. 

Input

The input consists of several instances. Each instance is described by a single line with four integers A, B, C, k separated by a single space. The integer k (1 <= k <= 32) is the number of bits of the control variable of the loop and A, B, C (0 <= A, B, C
< 2 ^k) are the parameters of the loop. 



The input is finished by a line containing four zeros. 

Output

The output consists of several lines corresponding to the instances on the input. The i-th line contains either the number of executions of the statement in the i-th instance (a single integer number) or the word FOREVER if the loop does not terminate. 

Sample Input

3 3 2 16
3 7 2 16
7 3 2 16
3 4 2 16
0 0 0 0

Sample Output

0
2
32766
FOREVER

注意基础知识：http://blog.csdn.net/u014665013/article/details/50858292

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <queue>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <set>
using namespace std;
typedef long long LL;
LL exgcd(LL a,LL b,LL &x,LL &y)  ///返回最大公约数
{
    if(b==0)
    {
        x=1;
        y=0;
        return a;
    }
    LL r=exgcd(b,a%b,x,y);
   // cout<<"x="<<x<<"  y="<<y<<endl;
    LL t=x;
    x=y;
    y=t-a/b*y;
    return r;
}
int main (){

LL A,B,C,k;
while(~scanf("%I64I64d%I64d%I64d%I64d",&A,&B,&C,&k)&&!(A==0&&B==0&&C==0&&k==0)){
    LL mmax=1LL<<k;
    LL a=C,b=mmax,c=(B-A+mmax)%mmax;   ///注意这里的b能通过是-mmax，因为这样到后面再求大于0的最小值就不好求了   但是也可以，下面的就要改了如下注释
    LL x,y;
    LL gcd = exgcd(a,b,x,y);
    if(c==0) {
        printf("%d\n",0);
        continue;
    }
    if(c%gcd==0){
        x=x*(c/gcd);
        LL r = b/gcd;
        x=(x%r+r)%r;   ///最小的正值   <span style="font-family: Arial, Helvetica, sans-serif;">x=-(x%r-r)%r</span>
        printf("%I64d\n",x);
    }
    else{
       printf("FOREVER\n");
    }
}
return 0;
}