### 2002 Canadian Computing Competition, Stage 2

## Day 2, Problem 1: Duathlon

A duathlon is a race that involves running *r* km and cycling *k* km. *n* contestants have entered the race; each contestant has different running and cycling speeds. One of the contestants has bribed the organizers to set *r* and *k* so that he can win by the maximum margin. You are to determine if this is possible and, if so, give *r* and *k*.

Note also that if the cheater ties with another contestant, it counts as a "win".

### Input

The first line of input contains an integer *t*, the total distance of the race, in km. That is, *r + k = t*. The next line contains an integer *n*, the number of competitors. For each contestant, a line follows with two real numbers giving the running and cycling speed for that contestant. The last line of input gives the running and cycling speed of the contestant who has bribed the organizers. You may assume *t* does not exceed 100 km/h and *n* does not exceed 20.

### Output

If it is possible to fix the race as describe above, print a message giving *r* and *k*, and the amount by which the cheater will win the race, accurate to two decimal places as in the sample below. If it is not possible, print "`The cheater cannot win.`

"

### Sample Input 1

`100`

3

10.0 40.0

20.0 30.0

15.0 35.0

### Sample Output 1

The cheater can win by 612 seconds with r = 14.29km and k = 85.71km.

### Sample Input 2

`100`

3

10.0 40.0

20.0 30.0

15.0 25.0

### Sample Output 2

`The cheater cannot win.`

All Submissions

Best Solutions

**Point Value:** 20

**Time Limit:** 2.00s

**Memory Limit:** 16M

**Added:** Apr 18, 2009

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

jimgaoon Dec 15, 2016 - 6:55:38 pm UTC Unique Answers?spencereiron Dec 17, 2016 - 4:50:16 am UTC Re: Unique Answers?Cueball1234on Oct 13, 2016 - 1:26:14 pm UTC Sample test case 1 has an integer amount of extra seconds?jargonon Oct 14, 2016 - 5:11:15 am UTC Re: Sample test case 1 has an integer amount of extra seconds?ImaxBlueon Apr 30, 2016 - 11:38:32 am UTC Small ErrorI assume it means t doesn`t exceed 100 km

ragulan5on Apr 29, 2009 - 12:53:50 am UTC Output 1SourSpinachon Apr 29, 2009 - 11:57:51 pm UTC Re: Output 1