Score: 600 points
Takahashi and Aoki are training for long-distance races in an infinitely long straight course running from west to east.
They start simultaneously at the same point and moves as follows towards the east:
How many times will Takahashi and Aoki meet each other, that is, come to the same point? We do not count the start of the run. If they meet infinitely many times, report that fact.
Input is given from Standard Input in the following format:
T_1 T_2 A_1 A_2 B_1 B_2
Print the number of times Takahashi and Aoki will meet each other.
If they meet infinitely many times, print infinity
instead.
1 2 10 10 12 4
1
They will meet just once, \frac{4}{3} minutes after they start, at \frac{40}{3} meters from where they start.
100 1 101 101 102 1
infinity
They will meet 101, 202, 303, 404, 505, 606, ... minutes after they start, that is, they will meet infinitely many times.
12000 15700 3390000000 3810000000 5550000000 2130000000
113
The values in input may not fit into a 32-bit integer type.