A sentence is a string of single-space separated words where each word can contain digits, lowercase letters, and the dollar sign '$'. A word represents a price if it is a sequence of digits preceded by a dollar sign.

• For example, "$100", "$23", and "$6" represent prices while "100", "$", and "$1e5" do not.

You are given a string sentence representing a sentence and an integer discount. For each word representing a price, apply a discount of discount% on the price and update the word in the sentence. All updated prices should be represented with exactly two decimal places.

Return a string representing the modified sentence.

Note that all prices will contain at most 10 digits.

 

Example 1:

Input: sentence = "there are $1 $2 and 5$ candies in the shop", discount = 50
Output: "there are $0.50 $1.00 and 5$ candies in the shop"
Explanation: 
The words which represent prices are "$1" and "$2". 
- A 50% discount on "$1" yields "$0.50", so "$1" is replaced by "$0.50".
- A 50% discount on "$2" yields "$1". Since we need to have exactly 2 decimal places after a price, we replace "$2" with "$1.00".

Example 2:

Input: sentence = "1 2 $3 4 $5 $6 7 8$ $9 $10$", discount = 100
Output: "1 2 $0.00 4 $0.00 $0.00 7 8$ $0.00 $10$"
Explanation: 
Applying a 100% discount on any price will result in 0.
The words representing prices are "$3", "$5", "$6", and "$9".
Each of them is replaced by "$0.00".

 

Constraints:

• 1 <= sentence.length <= 105
• sentence consists of lowercase English letters, digits, ' ', and '$'.
• sentence does not have leading or trailing spaces.
• All words in sentence are separated by a single space.
• All prices will be positive numbers without leading zeros.
• All prices will have at most 10 digits.
• 0 <= discount <= 100