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| #include<cstdio>
#include<cstring>
#include<algorithm>
#include<set>
using namespace std;
typedef long long LL;
const int maxn=10010;
int maxd,t,tt;
set<LL> sk;
LL ans[maxn],v[maxn];
LL gcd(LL a,LL b){
return b?gcd(b,a%b):a;
}
LL get_first(LL a,LL b){
return b/a+1;
}
bool better(int d){
for(int i=d;i>=0;--i)
if(v[i]!=ans[i]) return ans[i]==-1||v[i]<ans[i];
return false;
}
bool dfs(int d,LL from,LL a,LL b){
if(d==maxd){
if(b%a) return false;
v[d]=b/a;
if(sk.count(b/a)) return false;
if(better(d)) memcpy(ans,v,sizeof(LL)*(d+1));
return true;
}
bool ok=false;
for(LL i=max(from,get_first(a,b));;++i){
if(b*(maxd+1-d)<=i*a) break;
if(sk.count(i)) continue;
v[d]=i;
LL b2=b*i;
LL a2=a*i-b;
LL g=gcd(a2,b2);
if(dfs(d+1,i+1,a2/g,b2/g)) ok=true;
}
return ok;
}
int main(){
scanf("%d",&t);
while(t--){
LL a,b,k,sk0;
sk.clear();
scanf("%lld%lld%lld",&a,&b,&k);
while(k--) scanf("%lld",&sk0),sk.insert(sk0);
for(maxd=0;;++maxd){
memset(ans,-1,sizeof(ans));
if(dfs(0,get_first(a,b),a,b)) break;
}
printf("Case %d: %lld/%lld=",++tt,a,b);
for(int i=0;i<=maxd;++i){
if(i) printf("+");
printf("1/%lld",ans[i]);
}
printf("\n");
}
return 0;
}
|