44326d85.cpp

#include <bits/stdc++.h>
#define alive std::cout << "$LINE @" << __LINE__ << " ALIVE" << std::endl
#define watch(var) std::cout << "$ LINE @" << __LINE__ << " FUN @" << __FUNCTION__ \
                             << " VAR @" << (#var) << ": " << (var) << std::endl

using namespace std;

typedef int i32;
typedef unsigned int u32;
typedef long long i64;
typedef unsigned long long u64;
typedef double f64;
typedef long double f128;
typedef pair<int, int> pii;

template <typename Tp>
inline void read(Tp &x)
{
    x = 0;
    bool neg = false;
    char c = getchar();
    for (; !isdigit(c); c = getchar())
    {
        if (c == '-')
        {
            neg = true;
        }
    }
    for (; isdigit(c); c = getchar())
    {
        x = x * 10 + c - '0';
    }
    if (neg)
    {
        x = -x;
    }
}

template <typename Tp>
inline Tp gcd(Tp n, Tp m)
{
    while (m)
    {
        Tp t = n % m;
        n = m;
        m = t;
    }
    return n;
}

inline void solve()
{
    i64 a, b, c, d, p, m;
    read(a), read(b), read(c), read(d), read(p), read(m);
    auto calc = [&](i64 a, i64 b) -> i64 {
        if (a < 0LL || b < 0LL)
        {
            return 0LL;
        }
        ++a, ++b;
        i64 aD = a / p, bD = b / p, aM = a % p, bM = b % p;
        i64 res = (p * aD) * bD;
        res += aM * bD;
        res += bM * aD;
        --aM, --bM;
        if (aM > bM)
        {
            swap(aM, bM);
        }
        for (i64 sum = m, len = aM + bM; sum <= len; sum += p)
        {
            if (sum < aM)
            {
                res += sum + 1;
            }
            else if (aM <= sum && sum <= bM)
            {
                res += aM + 1;
            }
            else if (sum > bM)
            {
                res += len - sum + 1;
            }
        }
        return res;
    };
    i64 mole = calc(b, d) - calc(a - 1, d) - calc(b, c - 1) + calc(a - 1, c - 1),
        deno = (b - a + 1) * (d - c + 1);
    i64 div = gcd(mole, deno);
    mole /= div, deno /= div;
    printf("%lld/%lld\n", mole, deno);
}

int main()
{
    int T;
    read(T);

    for (int cas = 1; cas <= T; ++cas)
    {
        printf("Case #%d: ", cas);
        solve();
    }

    return 0;
}