## An Animal Contest 1 P2 - Alpaca Racing

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Points: 5 (partial)
Time limit: 0.6s
Python 1.5s
Memory limit: 256M

Author:
Problem types

You have decided to enter your alpaca into the annual Alpaca Racing Tournament! The race will be run around a track of length , and you will be competing against other alpacas. However, your alpaca is running slower than usual because it ate too many Cheetos got injured while training for the race. Desperate to win, you hack into the tournament software containing the speeds of all alpacas to see if there is a chance of victory. The speed of the alpaca is defined as , and your alpaca has speed . Soon, you realize that you have no chance of winning, but you have one more trick up your sleeve. You create a device that can reduce the speed of any alpaca, setting its new speed to . However, due to a bug in the device, it can only be used times. Your task is to find out if you can win if you use the device at most times. Note that winning means that you finish in the fastest time, meaning no ties.

#### Input Specification

The first line of input will contain 4 integers , all separated by a space.

The next lines will each contain , denoting the speed of the alpaca.

The final line of input will contain , denoting the speed of your alpaca.

#### Output Specification

You are to output YES if you can win the race outright after using the device at most times and NO otherwise.

Note: For this problem, you will NOT be required to pass the sample cases in order to receive points. In addition, you must pass all previous subtasks to earn points for a specific subtask.

#### Sample Input 1

2 12 3 30
100
50
50

#### Sample Output 1

YES

#### Explanation for Sample Output 1

The first alpaca finishes in hours, the second one finishes in hours and you finish in hours.

You use the device on the first alpaca twice, bringing his speed down to , then . The first alpaca now finishes in hours, which is slower than you. You also need to use the device once on the second alpaca. Using the device times allows you to win.

#### Sample Input 2

4 200 1 1
1000
12
2134
22
1

#### Sample Output 2

NO

• commented on Feb. 21, 2024, 1:16 a.m.

Nowhere in the problem do I read that the alpaca speeds (after using the device) must be integer values. This has a huge impact on the problem.

• commented on Feb. 23, 2024, 8:37 p.m.

the statement uses the floor function, which rounds down to the nearest integer.

• commented on Dec. 15, 2023, 11:03 p.m.

Im missing something, why does matter? As far as I could tell, the objective is to calculate the speed of the fastest opponents after using the device as much as possible and then check if your alpaca is the fastest afterwards. so why does matter? im sure it does have a part in the answer but i can't see how can someone help

• commented on Dec. 16, 2023, 1:31 p.m.

sorry i did not know editorials could be used like that