Men and Horses
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There are nm men living in a town. They have nh horses, each capable of carrying only one man at a time. All the men are supposed to attend a dinner party d km away from their house. They should start their journey together and reach destination in minimum time. Speed of each man is vm km/hour whereas speed of each horse (with or without somebody on back) is vh km/hour. You need to find the minimum time required to complete the journey? For simplicity you can assume the following things:
- No time is needed in riding a horse or getting down from a horse.
- The horses are very well trained to execute any instruction given to it.
- No time is needed for changing the direction of horse or man.
- The town and the dinner party location can be considered as two different points and all people and horses travel along the straight line connecting these two points.
- d (0 < d ≤ 10000)
- nm (1 < nm ≤ 1000)
- nh (0 < nh ≤ 1000)
- vm (0 < vm ≤ 20)
- vh (0 < vh ≤ 50)
Each input set consists of five integers d, nm, nh, vm, vh in a new line. Input ends with five 0s in a line. There will be at max 105+1 lines in the input
For each line of input except the last one produce one line of output. This line should print a fraction p by q, in p/q form. This denotes the minimum possible reaching time of all men. Here p and q must be relative prime.
Input 70 2 1 5 10 0 0 0 0 0 Output 49/5
|Tags||acm16kol, hard, kol_adm|
|Time Limit:||2 sec|
|Source Limit:||40000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.5|
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