Encryption

After the door opens, you rush into the secret base like a well-organized special ops unit. However as soon as you entered you notice that the place is completely empty apart from some pizza boxes and soda cans (but hey...it is at least 50 Ft each, so totally worth it). The terrorists left the place days ago and tried to remove every clue as to where. However at the back of one of the pizza boxes you notice some kind of a cipher which can maybe help. Your task is to break the encryption!

Input

The input contains two lines, each terminated by an end of line character:

• The first line is a string of arbitrary length consisting of the small and capital letters of the english alphabet and the space character (total of 53 possible characters).
• The second line contains 4 characters out of the 53 possible, separated by a single space character.

Output

The output is a single line which is the decrypted text.

Rules

The creation of the encrypted (input) text is the following:

• We number the possible 53 characters by: a=0,b=1,...,z=25,A=26,B=27,...,Z=51," "=52.
• We multiply each character (as a number) of the original message by the same K number and then add the same L number to it. Finally we reduce the achieved n number mod 53, which in programming simply means n%53.

Example: if K=3 and L=4, then from x=23 we get 3*23 + 4 = 73%53 = 20 = "u".
To get back the decrypted text (which is the required output) from the encrypted text (which is the first line of the input) we do the following:

• We subtract L from each character (as number) of the encrypted (input) text.
• Then we "divide" this number by K. However since every operation must be performed with integers between 0 and 52, then the division is not the classical division. The so-called "modular division" is done by first finding the number K' such that (K*K')%53 = 1. Then the division by K is equivalent to the multiplication by K', reduced of course modulo 53 (in programming %53).

Example: at the above example we can get back "x" from "u=20" by:

• "u"-L = 20-L = 16
• K' = 18, since (K*K')%53 = (3*18)%53 = 54%53 = 1
• So ((20-L)*18)%53 = (16*18)%53 = 288%53 = 23 = "x"

The only problem with the above algorithm is that we have no idea what are the values of K and L. However based on the second line of the input, we can calculate them!

• The second line of the input contains four characters, which give us 2 decrypted-encrypted character pairs.
• For example the "h n A z" line means that the unencrypted "h" has the encrypted pair of "n". Similarly the unencrypted "A" has the encrypted pair of "z".
• Based on this information we can calculate K and L by using a "system of equations", since the encryption is basically K*x + L = y, where x and y are the given unencrypted-encrypted pair and K and L are the unknowns. Since we have 2 unencrypted-encrypted letter pairs and we also have 2 unknowns, we can solve this system of equation. The only difficulty is that now every calculation is done modulo 53, but apart from the division (see above), every other mathematical operation is done exactly the same way as in the regular integers. We simply need to reduce the result by %53.

Example