CERC07N  Weird Numbers
Binary numbers form the principal basis of computer science. Most of you have heard of other systems, such as ternary, octal, or hexadecimal. You probably know how to use these systems and how to convert numbers between them. But did you know that the system base (radix) could also be negative. One assistant professor at the Czech Technical University has recently met negabinary numbers and other systems with a negative base. Will you help him to convert numbers to and from these systems.
A number N written in the system with a positive base R will always appear as a string of digits between 0 and R  1, inclusive. A digit at the position P (positions are counted from right to left and starting with zero) represents a value of R^P. This means the value of the digit is multiplied by R^P and values of all positions are summed together. For example, if we use the octal system (radix R = 8), a number written as 17024 has the following value:
1.8^4 + 7.8^3 + 0.8^2 + 2.8^1 + 4.8^0 = 1.4096 + 7.512 + 2.8+4.1 = 7700
With a negative radix R, the principle remains the same: each digit will have a value of (R)^P. For example, a negaoctal (radix R = 8) number 17024 counts as:
1.(8)^4 + 7.(8)^3 + 0.(8)^2 + 2.(8)^1 + 4.(8)^0 = 1.4096  7.512  2.8+4.1 = 500
One big advantage of systems with a negative base is that we do not need a minus sign to express negative numbers. A couple of examples for the negabinary system (R = 2):
decimal  negabinary  decimal  negabinary  decimal  negabinary 
10 9 8 7 6 5 4 
1010 1011 1000 1001 1110 1111 1100 
3 2 1 0 1 2 3 
1101 10 11 0 1 110 111 
4 5 6 7 8 9 10 
100 101 11010 11011 11000 11001 11110 
You may notice that the negabinary representation of any integer number is unique, if no "leading zeros" are allowed. The only number that can start with the digit "0", is the zero itself.
Input
The input will contain several conversions, each of them specified on one line. A conversion from the decimal system to some negativebase system will start with a lowercase word "to" followed by a minus sign (with no space before it), the requested base (radix) R, one space, and a decimal number N.
A conversion to the decimal system will start with a lowercase word "from", followed by a minus sign, radix R, one space, and a number written in the system with a base of R.
The input will be terminated by a line containing a lowercase word "end". All numbers will satisfy the following conditions: 2 <= R <= 10, 1 000 000 <= N <= 1 000 000 (decimal).
Output
For each conversion, print one number on a separate line. If the input used a decimal format, output the same number written in the system with a base R. If the input contained such a number, output its decimal value.
Both input and output numbers must not contain any leading zeros. The minus sign ""may only be present with negative numbers written in the decimal system. Any nonnegative number or a number written in a negativebase system must not start with it.
Example
Input to2 10 from2 1010 to10 10 to10 10 from10 10 end Output 11110 10 190 10 10
hide comments
unXled:
20120624 07:23:32
nice one.... 

15972125841321:
20120614 12:20:14
seriously.. had to check for 0 to get ac :D 

nagesh:
20110724 22:11:49
check out for 0...:D 
Added by:  Rafal 
Date:  20071116 
Time limit:  1.549s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Central European Programming Contest, Prague 2007 