1 #include <cstdio>  2 #include <cstring>  3 #include <cstdlib>  4 #include <cmath>  5 #include <cctype>  6 #include <time.h>  7 #include <string>  8 #include <set>  9 #include <map> 10 #include <queue> 11 #include <vector> 12 #include <stack> 13 #include <algorithm> 14 #include <iostream> 15 using namespace std; 16 #define PI acos( -1.0 ) 17 typedef long long ll; 18 typedef pair<int,int> P; 19 const double E = 1e-8; 20  21 ll a, b, c, d, p, m; 22  23 ll gcd( ll x, ll y ) 24 { 25     if( y == 0 ) 26         return x; 27     return gcd( y, x%y ); 28 } 29  30 void Solve() 31 { 32     ll ans = 0; 33     if( a+d >= b+c ) 34     { 35         ll ys1 = ( a + c ) % p; 36         ll x1 = ( m - ys1 + p ) % p; 37         ll num1 = ( x1 + a + c - m ) / p; 38         ll ys2 = ( b + c - 1 ) % p; 39         ll x2 = ( ys2 - m + p ) % p; 40         ll num2 = ( b + c - 1 - x2 - m ) / p; 41         ans += ( num2-num1 + 1 )*( x1+1 ) + ( num2-num1 + 1 )*( num2-num1 ) / 2 * p; 42  43         ys1 = ( b + c ) % p; 44         x1 = ( m- ys1 + p ) % p; 45         num1 = ( x1 + b + c - m ) / p; 46         ys2 = ( a + d ) % p; 47         x2 = ( ys2 - m + p ) % p; 48         num2 = ( a + d - x2 - m ) / p; 49         ans += ( num2 - num1 + 1 )*( b - a + 1 ); 50  51         ys1 = ( a + d + 1 ) % p; 52         x1 = ( m - ys1 + p ) % p; 53         num1 = ( x1 + 1 + a + d - m ) / p; 54         ys2 = ( b + d ) % p; 55         x2 = ( ys2 - m + p ) % p; 56         num2 = ( b + d - x2 - m ) / p; 57         ans += ( num2-num1+1 )*( x2+1 ) + ( num2-num1+1 )*( num2-num1 ) / 2 * p; 58     } 59     else 60     { 61         ll ys1 = ( a + c ) % p; 62         ll x1 = ( m - ys1 + p ) % p; 63         ll num1 = ( a + c + x1 - m ) / p; 64         ll ys2 = ( a + d - 1 ) % p; 65         ll x2 = ( ys2 - m + p ) % p; 66         ll num2 = ( a + d - 1 - x2 - m ) / p; 67         ans += ( num2-num1+1 )*( x1+1 ) + ( num2-num1+1 )*( num2-num1 ) / 2 * p; 68  69         ys1 = ( a + d ) % p; 70         x1 = ( m - ys1 + p ) % p; 71         num1 = ( a + d + x1 - m ) / p; 72         ys2 = ( b + c ) % p; 73         x2 = ( ys2 - m + p ) % p; 74         num2 = ( b + c - x2 - m ) / p; 75         ans += ( num2-num1+1 )*( d - c + 1 ); 76  77         ys1 = ( b + c + 1 ) % p; 78         x1 = ( m - ys1 + p ) % p; 79         num1 = ( b + c + 1 + x1 - m ) / p; 80         ys2 = ( b + d ) % p; 81         x2 = ( ys2 - m + p ) % p; 82         num2 = ( b + d - x2 - m ) / p; 83         ans += ( num2-num1+1 )*( x2+1 ) + ( num2-num1+1 )*( num2-num1 ) / 2 * p; 84     } 85     ll num = ( b-a+1 )*( d-c+1 ); 86     ll mod = gcd( num, ans ); 87     printf( "%I64d\/%I64d\n", ans/mod, num/mod ); 88 } 89  90 int main() 91 { 92     int T, tcase = 0; 93     scanf( "%d", &T ); 94     while( T-- ) 95     { 96         scanf( "%I64d%I64d%I64d%I64d%I64d%I64d", &a, &b, &c, &d, &p, &m ); 97         printf( "Case #%d: ", ++tcase ); 98         Solve(); 99     }100     return 0;101 }