1 /*
2 POJ1061 青蛙的约会
3 http://poj.org/problem?id=1061
4 扩展欧几里得
5
6 原题为求t使得,存在l满足
7 (x+mt)-(y+nt)=cl
8 即求
9 cl+(n-m)t=x-y
10 *
11 *
12 *
13 */
14
15 #include <cstdio>
16 #include <cmath>
17 using namespace std;
18 long long ex_gcd(long long a,long long b,long long &x,long long &y)//solve x,y in a*x+b*y=ex_gcd(a,b,x,y)=gcd(a,b);
19 {
20 if(b==0LL)
21 {
22 x=1LL;
23 y=0LL;
24 return a;
25 }
26 long long ans=ex_gcd(b,a%b,x,y);
27 long long tmp=x;
28 x=y;
29 y=tmp-a/b*y;
30 return ans;
31 //x = x0 + (b/gcd)*t
32 //y = y0 – (a/gcd)*t
33
34 }
35 int main()
36 {
37 long long x,y,m,n,l;
38 scanf("%lld%lld%lld%lld%lld",&x,&y,&m,&n,&l);
39 long long a=l,b=n-m;
40 l=x-y;
41 long long xx,yy;
42 long long gcd=ex_gcd(a,b,xx,yy);
43 if(l%gcd)
44 {
45 printf("Impossible\n");
46 return 0;
47 }
48
49 long long r=l/gcd;
50 //while(xx<=0)
51 //{
52 //xx=xx+b/gcd;
53 //yy=yy-a/gcd;
54 //}
55 yy=yy*r;
56 a=a/gcd;
57 long long t=yy%a;
58 while(t<0)
59 t+=a;
60 printf("%lld\n",t);
61 return 0;
62 }
