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Problem 1007
Do the Untwist
Time Limit: 1000ms
Memory Limit: 65536kb Description
Cryptography deals with methods of secret communication that
transform a message (the plaintext) into a disguised form (the
ciphertext) so that no one seeing the ciphertext will be able
to figure out the plaintext except the intended recipient.
Transforming the plaintext to the ciphertext is encryption;
transforming the ciphertext to the plaintext is decryption.
Twisting is a simple encryption method that requires that the
sender and recipient both agree on a secret key k, which is a
positive integer.The twisting method uses four arrays: plaintext and ciphertext are arrays of characters, and plaincode and ciphercode are arrays of integers. All arrays are of length n, where n is the length of the message to be encrypted. Arrays are origin zero, so the elements are numbered from 0 to n - 1. For this problem all messages will contain only lowercase letters, the period, and the underscore (representing a space). The message to be encrypted is stored in plaintext. Given a key k, the encryption method works as follows. First convert the letters in plaintext to integer codes in plaincode according to the following rule: '_' = 0, 'a' = 1, 'b' = 2, ..., 'z' = 26, and '.' = 27. Next, convert each code in plaincode to an encrypted code in ciphercode according to the following formula: for all i from 0 to n - 1, ciphercode[i] = (plaincode[ki mod n] - i) mod 28.(Here x mod y is the positive remainder when x is divided by y. For example, 3 mod 7 = 3, 22 mod 8 = 6, and -1 mod 28 = 27. You can use the C '%' operator or Pascal 'mod' operator to compute this as long as you add y if the result is negative.) Finally, convert the codes in ciphercode back to letters in ciphertext according to the rule listed above. The final twisted message is in ciphertext. Twisting the message cat using the key 5 yields the following:
Input
The input contains one or more test cases, followed by a line
containing only the number 0 that signals the end of the file.
Each test case is on a line by itself and consists of the key k, a
space, and then a twisted message containing at least one and at most 70
characters. The key k will be a positive integer not greater than
300.
Output
For each test case, output the untwisted message on a line
by itself.Note: you can assume that untwisting a message always yields a unique result. (For those of you with some knowledge of basic number theory or abstract algebra, this will be the case provided that the greatest common divisor of the key k and length n is 1, which it will be for all test cases.) Sample Input
5 cs. 101 thqqxw.lui.qswer 3 b_ylxmhzjsys.virpbkr 0 Sample Output
cat this_is_a_secret beware._dogs_barking |