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.
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.
Sample Input Output for Sample Input
Problem source: Iranian Contest
Special Thanks Monirul Hasan, EPS.