学步园

扩展GCD

因为 跳跃的次数相同 ,设跳了S次。

所以就有  s * m - (x -y) - s * n = l * k; 

转换一下就是 s *(m - n) + k * l = x - y 

就会发现是一个扩展GCD

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
typedef long long LL;
LL Gcd(LL a,LL b){
    LL r = a % b;
    while(r){
        a = b;
        b = r;
        r = a % b;
    }
    return b;
}
void Ex_Gcd(LL a,LL b,LL &x,LL &y){
    if(!b){
        x = 1;
        y = 0;
        return ;
    }
    Ex_Gcd(b,a % b,x,y);
    LL temp = x;
    x = y;
    y = temp - a / b * y;
    return ;
}
int main(){
    LL x,y,m,n,l;
    while(~scanf("%I64d%I64d%I64d%I64d%I64d",&x,&y,&m,&n,&l)){
        LL a = n - m,c = x - y;
        LL d = Gcd(a,l);
        if(c % d != 0) printf("Impossible\n");
        else{
            LL x1,y1;
            Ex_Gcd(a,l,x1,y1);
            LL k = c / d;
            x1 *= k;
            x1 %= l;
            while(x1 <= 0) x1 +=l;
            printf("%I64d\n",x1);

        }
    }
    return 0;
}