An Animal Contest 1 P2 - Alpaca Racing

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

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 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.


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

Sample Output 1


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

Sample Output 2



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