Description

　　For this question, your program is required to process an input string containing only ASCII characters between ‘0’ and ‘9’, or between ‘a’ and ‘z’ (including ‘0’, ‘9’, ‘a’, ‘z’).

　　Your program should reorder and split all input string characters into multiple segments, and output all segments as one concatenated string. The following requirements should also be met,

　　1. Characters in each segment should be in strictly increasing order. For ordering, ‘9’ is larger than ‘0’, ‘a’ is larger than ‘9’, and ‘z’ is larger than ‘a’ (basically following ASCII character order).

　　2. Characters in the second segment must be the same as or a subset of the first segment; and every following segment must be the same as or a subset of its previous segment.

　　Your program should output string “” when the input contains any invalid characters (i.e., outside the ’0′-’9′ and ‘a’-’z’ range).

　　Input

　　Input consists of multiple cases, one case per line. Each case is one string consisting of ASCII characters.

　　Output

　　For each case, print exactly one line with the reordered string based on the criteria above.

　　樣例輸入

　　aabbccdd

　　007799aabbccddeeff113355zz

　　1234.89898

　　abcdefabcdefabcdefaaaaaaaaaaaaaabbbbbbbddddddee

　　樣例輸出

　　abcdabcd

　　013579abcdefz013579abcdefz

　　abcdefabcdefabcdefabdeabdeabdabdabdabdabaaaaaaa

　　Description

　　Consider a string set that each of them consists of {0, 1} only. All strings in the set have the same number of 0s and 1s. Write a program to find and output the K-th string according to the dictionary order. If such a string doesn’t exist, or the input is not valid, please output “Impossible”. For example, if we have two ‘0’s and two ‘1’s, we will have a set with 6 different strings, {0011, 0101, 0110, 1001, 1010, 1100}, and the 4th string is 1001.

　　Input

　　The first line of the input file contains a single integer t (1 ≤ t ≤ 10000), the number of test cases, followed by the input data for each test case.

　　Each test case is 3 integers separated by blank space: N, M(2 <= N + M <= 33 and N , M >= 0), K(1 <= K <= 1000000000). N stands for the number of ‘0’s, M stands for the number of ‘1’s, and K stands for the K-th of string in the set that needs to be printed as output.

　　Output

　　For each case, print exactly one line. If the string exists, please print it, otherwise print “Impossible”.

　　樣例輸入

　　3

　　2 2 2

　　2 2 7

　　4 7 47

　　樣例輸出

　　0101

　　Impossible

　　01010111011

　　Description

　　Find a pair in an integer array that swapping them would maximally decrease the inversion count of the array. If such a pair exists, return the new inversion count; otherwise returns the original inversion count.

　　Definition of Inversion: Let (A[0], A[1] … A[n]) be a sequence of n numbers. If i < j and A[i] > A[j], then the pair (i, j) is called inversion of A.

　　Example:

　　Count(Inversion({3, 1, 2})) = Count({3, 1}, {3, 2}) = 2

　　InversionCountOfSwap({3, 1, 2})=>

　　{