Light OJ 1064 / DP - Probability

/***
 created: 2022-08-27-02.11.17
***/

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename U> using ordered_set=tree<U, null_type,less<U>,rb_tree_tag,tree_order_statistics_node_update>;
#define ll long long
#define test int tt; cin>>tt; for(int cs=1;cs<=tt;cs++)
#define get_lost_idiot return 0
#define nl '\n'

ll dp[27][6*25 + 5];
ll n,x;

ll solve(ll in, ll sum)
{
    if(in>=n)
    {
        return sum>=x;
    }

    if(dp[in][sum]!=-1) return dp[in][sum];

    ll ans=0;

    for(ll i=1;i<=6;i++)
    {
        ans+=solve(in+1,sum+i);
    }

    return dp[in][sum]=ans;
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    test
    {
        ll p,q,i,j,k,l;

        cin>>n>>x;

        memset(dp,-1,sizeof dp);

        p=solve(0,0);
        q=pow(6,n);

        l=__gcd(p,q);

        p/=l,q/=l;

        cout<<"Case "<<cs<<": "<<p;

        if(q>1) cout<<"/"<<q<<nl;
        else cout<<nl;

    }



    get_lost_idiot;
}