Practice Cryptography and Arithmetic with the exercise "The Prime Twins

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

Part one : https://www.codingame.com/training/easy/the-prime-twins---part-one

Context :
五 and 七, two brilliant young students in middle school, have just finished creating their own secret language during the holidays. Proud of their creation, they speak confidently, convinced that no one will ever be able to decipher their messages.

Encryption principles :
• i denotes the integer between a pair of prime twins. For example, between 5 and 7, i = 6.
• key represents the secret key agreed upon by 五 and 七.

Transformation rules :
A is transformed into key + key. For subsequent letters like B and beyond, key is added to the integer located between the closest pair of prime twins that is strictly greater than the previous value. For example, if the previous value was i, the search for the next pair of twins starts from i + 1.

Example :
If key = 3, A = 3 + 3 = 6. For B, the search for prime twins starts strictly above 6, and the closest twins will be 11 and 13, so i = 12 and B = 3 + 12 = 15. For C, starting strictly above 15, the next twins will be 17 and 19, so i = 18 and C = 3 + 18 = 21.

Input format :
For an ENCODE operation, message contains only upper case letters and spaces.
For a DECODE operation, message contains only upper case hexadecimal values and the upper case letter G.

Output format :
The resulting integers are then converted to hexadecimal in upper case, separated by G or GG for space. For example, ABC is transformed into 6, 15, 21, which is then converted to 6GFG15.

Error case :
If message does not comply with its respective input format, you must return ERROR !!.

Goal :
Develop code to decode or encode the secret language of 五 and 七.

Input

Line 1: string operation ENCODE/DECODE
Line 2: integer key Secret key agreed upon by 五 and 七
Line 3: string message

Output

encoded or decoded upper case letter message / "ERROR !!"

Constraints

2 <= key <= 5*10⁶
message contains only upper case letters and spaces

Example

Input

ENCODE
3
ABC

Output

6GFG15

Solve it

A higher resolution is required to access the IDE