denotes a set called the key space. Any element of is called a key.

Each element uniquely determines a bijection from to , denoted by . The is called an encryption function. Similarly for each , we have a bijection from to , denoted by , and it is called a decryption function.

For example, consider the same shifting function that we dealt with in the previous challenge. Now, suppose the amount of shifting we do is some . In the last challenge, . Then is a valid key representing the bijective function .

For this task, consider a message that consists of decimal digits and a key, , which operates by shifting each digit by places. Find the corresponding ciphertext.

Constraints