Problem A
The Fun Number System
Input: standard input
Output: standard output
Time Limit: 1 second
In a k bit 2’s complement number,
where the bits are indexed from 0 to k –1, the weight of the most
significant bit (i.e., in position k –1), is –2k–1 , and the weight of a bit in any position i (0 =i < k –1)
is 2i . For example, a 3 bit number 101 is evaluated as -22+0+20
= -3 and 011 as –0+21+20 = 3. A negatively weighted
bit is called a negabit (such as the most significant bit in a 2’s
complement number), and a positively weighted bit is called a posibit.
A Fun number system is a positional binary number system, where each bit can be either a negabit, or a posibit. For example consider a 3-bit fun number system Fun3, where bits in positions 0, and 2 are posibits, and the bit in position 1 is a negabit. (111)Fun3 is evaluated as 22 –21 + 1 = 3. Now you are going to have fun with the Fun number systems! You are given the description of a k-bit Fun number system Funk, and an integer N (Maybe negative). You should determine the k bits of a representation of N in Funk, or report that it is not possible to represent the given N in the given Funk. For example, a representation of –1 in the Fun3 number system (defined above), is 011 (evaluated as 0–21+20 ), and representing 6 in Fun3 is impossible.
Input
The first line of
the input file contains a single integer t (0 <t =100), the number of
test cases, followed by the input data for each test case.
Each test case is given in three consecutive lines. In the first line there is a positive integer k(1<=k <=64). In the second line of a test data there is a string of length k, composed only of letters n , and p , describing the Fun number system for that test data, where each n (p) indicates that the bit in that position is a negabit (posibit). The third line of each test data contains an integer N (-263 =N<263), the number to be represented in the Funk number by your program.
For each test data, you should print one line containing
either a k-bit string representing the given number N in the Funk number system, or the
word Impossible, when it
is impossible to represent the given number.
2 3 pnp 6 4 ppnn 10 |
Impossible 1110 |
Problem source: Iranian
Contest
Special Thanks Monirul
Hasan, EPS.