扩展欧几里得

扩展欧几里得求不定方程

题目链接：http://poj.org/problem?id=1061

$x\times a+y\times b=gcd(a,b) \rightarrow y\times b+\left ( x-\frac{a}{b}\times y \right )\times \left ( a\%b \right )=gcd(a,b)$

对于知道特解$x_{1}$和$y_{1}$通解为：$x=x_{1}-t\times  \frac{b}{gcd(a,b)} $   $y=y_{1}-t\times \frac{a}{gcd(a,b)}$  $t\epsilon Z$

#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
#define ll long long
ll gcdd(ll a,ll b,ll &x,ll &y)//    a*x+b*y=gcd(a,b)
{
    if(b==0)
    {
        x=1;
        y=0;
        return a;
    }
    ll res=gcdd(b,a%b,x,y);
    ll temp=x;
    x=y;
    y=temp-a/b*y;
    return res;
}
int main()
{
    ll x,y,m,n,L,k,T;
    while(cin>>x>>y>>m>>n>>L)
    {
        ll gcd=gcdd(m-n,L,k,T);
        if((y-x)%gcd!=0)
        {
            cout<<"Impossible"<<endl;
        }
        else
        {
            ll mmp=(y-x)/gcd;
            k*=mmp;
            ll k0=k%abs(L/gcd);
            if(k0<0)k0+=abs(L/gcd);
            cout<<k0<<endl;
        }
    }
    return 0;
}