Permutation of a given string can be done in different ways. In order to get different permutations of a string, when all characters in the string are different, Donald E. Knuth gave the following process. To get all the permutations of a n character string (a1a2an), using each permutation a1, a2?an-1, we can form n others by inserting an?(nth character) in all possible places. Thus we get n! permutations of that string. For example, to generate all permutations of ACB? we first start with A? then insert C?and then insert B?

Col1

Col2

Col3

Permutation Index

A

CA

 

AC

BCA

CBA

CAB

BAC

ABC

ACB

1

2

3

4

5

6

So we see that using above technique, the permutations of ACB?are generated in a particular order. Here 2nd permutation of ACB?is the string CBA?or permutation index of CBA?is 2. In this problem you will be given a string and a permutation index, I. You have to find the I'th permutation of the given string.

Input

First line of the input file will contain an integer denoting the number of test cases to follow. For each test case there will be two lines. First line of each test case will contain a string of length less than or equal to 26. The characters of the string will be all upper case letters and different. Next line will contain a permutation index, I. Range of I is from 1 to min(n!,2^31-1), where n is the length of the string.


Output

For each test case, print the I'th permuted string of the given string in a line. Look at Sample input and output for details.

 

Sample Input

4 ACB 2 ABC 1 ABC 6 ABCD 12

Sample Output

CBA CBA ABC BACD

Author : S. M. Shahed Nejhum

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