Code and design the following program requirements:

This program is a "guessing game" program. The program will generate a random integer between $1$ and $10000,$ inclusive. The program should prompt the user to enter a guess. For each guess, the program will output $$HIGHER$$ if the user's guess is lower than the target, $$LOWER$$ if the user's guess is higher than the target, or $$WINNER$$ if the user guesses the target. Each time the program prompts the user for a new guess, it should calculate and display the eligible range of values.$$

Sample output:

Please enter a number between $1$ and $10000$: $5000$

Your guess is too high, try again.

Please enter a number between $1$ and $5000$: $2500$

Your guess is too high, try again.

Please enter a number between $1$ and $2500$: $1500$

Your guess is too low, try again.

Please enter a number between $1500$ and $2500$: $2000$

Your guess is too high, try again.

Please enter a number between $1500$ and $2000$: $1600$

Your guess is too low, try again.

Note: Ensure that the prompt displays the current range of valid numbers.