You have decided to enter your alpaca into the annual Alpaca Racing Tournament! The race will be run around a track of length 
~D~, and you will be competing against 
~N~ 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 
~i^\text{th}~ alpaca is defined as 
~a_i~, and your alpaca has speed 
~P~. 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 
~\left\lfloor \text{speed} \times \frac{100-X}{100} \right\rfloor~. However, due to a bug in the device, it can only be used 
~K~ times. Your task is to find out if you can win if you use the device at most ~K~ times. Note that winning means that you finish in the fastest time, meaning no ties.
Constraints
For all subtasks:
~1 \le N, K \le 10^6~
~1 \le D, P, a_i \le 10^{16}~
~1 \le X \le 100~
Subtask 1 [10%]
~X = 100~
Subtask 2 [90%]
No additional constraints.
Input Specification
The first line of input will contain 4 integers 
~N, D, K, X~, all separated by a space.
The next ~N~ lines will each contain ~a_i~, denoting the speed of the ~i^\text{th}~ alpaca.
The final line of input will contain ~P~, 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 ~K~ 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 
~12/100 = 0.12~ hours, the second one finishes in 
~12/50 = 0.24~ hours and you finish in ~12/50 = 0.24~ hours.
You use the device on the first alpaca twice, bringing his speed down to 
~\lfloor 100 \times \frac{100-30}{100} \rfloor = 70~, then 
~\lfloor 70 \times \frac{100-30}{100} \rfloor = 49~. The first alpaca now finishes in 
~12/49 = 0.245~ hours, which is slower than you. You also need to use the device once on the second alpaca. Using the device 
~3~ times allows you to win.
Sample Input 2
4 200 1 1
1000
12
2134
22
1
Sample Output 2
NO
Comments
If you get NumberFormatException, make sure that D, P, and ai are longs instead of ints otherwise the input won't get in properly.
I still don't get why is the distance needed when we can just compare speeds
I spent an hour rethinking and verifying the correctness of my program and I kept coming back to the same result — it was correct in all respects. My output was the culprit (instead of "YES", my output was "Yes"). The judge is very strict (I'm not complaining, I'm very much aware).
Make sure that your output is EXACTLY as described in the problem statement before you submit your code.
Also, the first thing you should check when you get WA (especially on the first test case in any problem) is that your output is EXACTLY as described.
I'm stumped. According to the judge I'm generating output (YES) but I'm also getting a TLE (Python). Huh? Do you get output if you encounter a TLE. Or is it just that my program is generating the output around the time cutoff?
Don't quote me on this, but I think it's the latency between the judge terminating the code and the code stopping - your code generated an output in that time frame
Thank you.
[edit] DMOJ's optimizations relevant to the judge were required for my python submission: https://dmoj.ca/tips/#python-main. But, now that I can see other solutions I see that the optimizations are not required for less convoluted solutions than mine.
because it ate too many Cheetos🤣
When changing the speed another alpaca, remember to floor the alpaca's speed to pass batch #2 test case #7.
Also, Java users should use long integers, and c++ users should use long long integers to prevent integer overflow to pass batch #2 test case #1.
Ironically, flooring all the time is what prevented me from solving the problem.
yeah I failed on the first try because I was too rushed at the time and forgot to floor.