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Cryptographydeals with methods of secret communication that transform a message (theplaintext) into a disguised form (theciphertext) 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 isencryption; transforming the ciphertext to the plaintext isdecryption.Twistingis a simple encryption method that requires that the sender and recipient both agree on a secret keyk, which is a positive integer.

The twisting method uses four arrays:plaintextandciphertextare arrays of characters, andplaincodeandciphercodeare arrays of integers. All arrays are of lengthn, wherenis the length of the message to be encrypted. Arrays are origin zero, so the elements are numbered from 0 ton-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 inplaintext. Given a keyk, the encryption method works as follows. First convert the letters inplaintextto integer codes inplaincodeaccording to the following rule: '_' = 0, 'a' = 1, 'b' = 2, ..., 'z' = 26, and '.' = 27. Next, convert each code inplaincodeto an encrypted code inciphercodeaccording to the following formula: for allifrom 0 ton-1,

ciphercode[i] = (plaincode[kimodn]-i) mod 28.

(Herexmodyis the positive remainder whenxis divided byy. 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 addyif the result is negative.) Finally, convert the codes inciphercodeback to letters inciphertextaccording to the rule listed above. The final twisted message is inciphertext. Twisting the messagecatusing the key 5 yields the following:

Array	0	1	2
plaintext	'c'	'a'	't'
plaincode	3	1	20
ciphercode	3	19	27
ciphertext	'c'	's'	'.'

Your task is to write a program that canuntwistmessages,i.e., convert the ciphertext back to the original plaintext given the keyk. For example, given the key 5 and ciphertext 'cs.', your program must output the plaintext 'cat'.

The input file 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 keyk, a space, and then a twisted message containing at least one and at most 70 characters. The keykwill be a positive integer not greater than 300. 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 keykand lengthnis 1, which it will be for all test cases.)

Example input:

5 cs.101 thqqxw.lui.qswer3 b_ylxmhzjsys.virpbkr0

Example output:

catthis_is_a_secretbeware._dogs_barking

#include<iostream>
using namespace std;
#include<string.h>
int main()
{
char a[72];
int k;
while(cin>>k&&k!=0)
{
cin>>a;
int n,i,j;
int b[72];
char c[72];
n=strlen(a);
for(i=0;i<n;i++)
{
if(a[i]=='_')
b[i]=0;
else if(a[i]=='.')
b[i]=27;
else
{
b[i]=int(a[i])-96;

}

}
for(i=0;i<n;i++)
{
if(b[i]+i>=28)
b[i]=(b[i]+i)%28;
else
b[i]=b[i]+i;
}
for(i=0;i<n;i++)
{
if(b[i]==0)
{
j=(k*i)%n;
c[j]='_';
}
else if(b[i]==27)
{
j=(k*i)%n;
c[j]='.';
}
else
{
j=(k*i)%n;
c[j]=b[i]+96;
}
}
for(j=0;j<n;j++)
{
cout<<c[j];
}
cout<<endl;

}
return 0;

}