连分数(分数类模板) uva6875

//连分数(分数类模板) uva6875
// 题意：告诉你连分数的定义。求连分数，并逆向表示出来
// 思路：直接上分数类模板。要注意ai可以小于0

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
using namespace std;
#define LL long long
typedef pair<int,int> pii;
const int inf = 0x3f3f3f3f;
const int MOD = 998244353;
const int N = 1020;
const int maxx = 200010; 
#define clc(a,b) memset(a,b,sizeof(a))
const double eps = 0.025;
void fre() {freopen("in.txt","r",stdin);}
void freout() {freopen("out.txt","w",stdout);}
inline int read() {int x=0,f=1;char ch=getchar();while(ch>'9'||ch<'0') {if(ch=='-') f=-1; ch=getchar();}while(ch>='0'&&ch<='9') {x=x*10+ch-'0';ch=getchar();}return x*f;}

struct fr{
    LL a,b;
    fr(LL a_,LL b_){
        LL g=__gcd(a_,b_);
        a=a_/g;
        b=b_/g;
    }
    fr operator + (const fr &x){
        return fr(a*x.b+b*x.a,b*x.b);
    }
    fr operator -(const fr &x){
        return fr(a*x.b-x.a*b,b*x.b);
    }
    fr operator *(const fr &x){
        return fr(a*x.a,b*x.b);
    }
    fr operator /(const fr &x){
        return fr(a*x.b,b*x.a);
    }
    void add(LL x){
        a+=b*x;
    }
    LL split(){
        LL r=a/b;
        a%=b;
        if(a<0){
            r--;
            a+=b;
        }
        return r;
    }
    void inv(){
        std::swap(a,b);
        if(b<0){
            a=-a;
            b=-b;
        }
    }
    operator bool(){
        return a;
    }
};
LL in[11];
int n,m;
int main(){
    int cas=1;
    while(~scanf("%d%d",&n,&m),n&&m){
        for(int i=1;i<=n;i++) scanf("%lld",&in[i]);
        fr x(0,1);
        for(int i=n;i>=1;i--) {
           x.add(in[i]);
           if(i!=1)x.inv();
        }

        for(int i=1;i<=m;i++) scanf("%lld",&in[i]);
        fr y(0,1);
        for(int i=m;i>=1;i--) {
            y.add(in[i]);
            if(i!=1) y.inv();
        }

        fr ad=x+y,sub=x-y,mul=x*y,div=x/y;
        printf("Case %d:
",cas++);
        
        ad.inv();
        while(ad){
            ad.inv();
            printf("%lld",ad.split());
            if(ad){
                printf(" ");
            }
        }
        printf("
");

        sub.inv();
        while(sub){
            sub.inv();
            printf("%lld",sub.split());
            if(sub){
                printf(" ");
            }
        }
        printf("
");

        mul.inv();
        while(mul){
            mul.inv();
            printf("%lld",mul.split());
            if(mul){
                printf(" ");
            }
        }
        printf("
");

        div.inv();
        while(div){
            div.inv();
            printf("%lld",div.split());
            if(div){
                printf(" ");
            }
        }
        printf("
");
    
    }
    return 0;
}