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):
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.
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, -1000000≤N≤1000000 (decimal).
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 non-negative number or a number written in a negative-base system must not start with it.
to-2 10 from-2 1010 to-10 10 to-10 -10 from-10 10 end
11110 -10 190 10 -10