73 lines
1.2 KiB
C++
73 lines
1.2 KiB
C++
#include<cstdio>
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#include<cstring>
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#include<set>
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using namespace std;
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typedef long long ll;
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const int maxn=100000+10;
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set<ll> st;
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int maxed;
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bool ok;
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ll v[maxn],res[maxn];
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ll gcd(ll a,ll b){return b==0?a:gcd(b,a%b);}
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inline ll get_first(ll a,ll b){return b/a+1;}
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bool better(int d)
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{
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for(int i=d;i>=0;i--)
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if(res[i]!=v[i])
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return res[i]==-1||v[i]<res[i];
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return false;
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}
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void dfs(int pos,ll from,ll a,ll b)
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{
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if(pos==maxed)
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{
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if(b%a||st.count(b/a)) return;
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v[pos]=b;
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if(better(pos)) memcpy(res,v,(pos+1)<<3);
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ok=true;
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return;
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}
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from=max(from,get_first(a,b));
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for(int i=from;;i++)
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{
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if(a*i>=b*(maxed-pos+1)) return;
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if(st.count(i)) continue;
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v[pos]=i;
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ll t1=a*i-b,t2=b*i;
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ll g=gcd(t1,t2);
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dfs(pos+1,i+1,t1/g,t2/g);
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}
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return;
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}
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ll a,b,x;
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int n,T,kase;
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int main()
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{
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#ifdef local
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freopen("pro.in","r",stdin);
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#endif
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scanf("%d",&T);
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while(T--)
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{
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st.clear();
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scanf("%lld %lld %d",&a,&b,&n);
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for(int i=0;i<n;i++)
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{
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scanf("%lld",&x);
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st.insert(x);
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}
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ok=false;
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for(maxed=1;;maxed++)
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{
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memset(res,-1,sizeof(res));
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dfs(0,get_first(a,b),a,b);
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if(ok) break;
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}
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printf("Case %d: %lld/%lld=",++kase,a,b);
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printf("1/%lld",res[0]);
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for(int i=1;i<=maxed;i++) printf("+1/%lld",res[i]);
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puts("");
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}
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return 0;
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}
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