Wily Hacker finds on his chief's desk the encryption scheme of the chief's most important messages. He also finds, in his chief's computer, files with cryptograms and the associated encryption keys. He wishes to write a program for decrypting these cryptograms.

Wily read a book about modern encryption. He discovered that twenty years ago cryptography became the subject of many applications in the domain of computer data security. More and more persons wish to make their messages and files confidential. A cipher is a secret method of transforming plaintext (message) into ciphertext (cryptogram). This operation, called encryption, is controlled by an encryption key. There must exist the reverse transformation, called decryption, which transforms ciphertext into plaintext using a decryption key, which is derived using the encryption key.

Wily observes that the algorithm shown in the figure encrypts the 64-bit message M into the 64-bit cryptogram C, under the control of the 64-bit key K.

The encryption function uses 3 types of operations:

• exclusive-or, marked with the symbol ;
• addition module 216, marked with the symbol +;
• left circular shift, with a number of positions indicated by the input K, marked with the symbol .

The algorithm uses the following notations:

• M_i, i=1...4 represents four 16-bit blocks of plaintext;
• C_i, i=1...4 represents four 16-bit blocks of cryptogram;
• K_i, i=1...4 represents four 16-bit blocks of the encryption key.

Your task is to write a program that obtains plain messages from cryptograms and decryption keys by discovering a suitable scheme, just like Wily Hacker did.

Input 

Output 

Sample Input 

85bfa0242caa796e    1111222233334444
4c0d17279cbf4222    abcdabcdabcdabcd

Sample Output 

TEACHERS
STUDENTS