解同余方程

#include<cstdio>

 

long long mod(long long a,long long b)

{ return (a % b + b) % b; }

 

struct triple { long long d,x,y; };

 

long long Euclid(long long a,long long b)

{

       if(b == 0) return a;

       else return Euclid(b,mod(a,b));

}

 

triple Extended_Euclid(long long a,long long b)

{

       triple result;

       if(b == 0)

       { result.d = a; result.x = 1; result.y = 0; }

       else

       {

          triple ee = Extended_Euclid(b,mod(a,b));

          result.d = ee.d;

          result.x = ee.y;

          result.y = ee.x - (a/b)*ee.y;

       }

       return result;

}

 

long long MLES(long long a,long long b,long long n)

{

       triple ee = Extended_Euclid(a,n);

       if(mod(b,ee.d)) return -1;

       else return mod((ee.x * (b / ee.d)),n/ee.d);

}

 

int main()

{

     long long x, y, m, n, l;

     while(scanf("%I64d%I64d%I64d%I64d%I64d",&x,&y,&m,&n,&l) != EOF)

       {

              long long mles;

              mles = MLES(m-n,y-x,l);

             /*此处输入三个参数设为 a，b，n 可求得(ax-b)%n=0的最小解。

                如果返回-1，则表示此方程无解。*/

              if(mles < 0)

                     printf("Impossible\n");

              else

                     printf("%I64d\n",mles);

       }

     return 0;

}