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Find the smallest number that can be framed using the series created by the digits obtained by raising the given number  (  "a"  ) to the power from 1 to  n  i.e.  a^1 , a^2 , a^3 .......a^n . We get  b1,b2 , b3 , ........... bn . 
Using all the digits  ( including repeating ones )  that appear in
b1 ,b2 , b3 .... bn . Frame a number that contains all the digits ( including repeating ones )  and find out the combination of digits that make the smallest number of all possible combinations. Excluding or neglecting zeroes  ( " 0 " )  . 

 

Input: The first line contains a number T i.e numbers of  test cases . Followed by each test case that contains two integers "a" and "n" . 


Output: Output of each test case contains an integer which is the smallest number out of all combinations .


Constraints:   

1 < = T < = 350
0 < = n < =  5
0 < = a < = 90 


Example:

Input 
4
9 4
5 1
6 5
90 4

Output:

1125667899
5
11223666667779
1125667899

Explanation :
Test case 1: 9 3 
9^1 = 9
9^2 = 81
9^3 = 729
9^4  = 6561 
9 81 729 6561
We get  9817296561 .
Using 9817296561 number we need to find the smallest possible number that can be framed using other combinations of the same
number .
1298796561
8799265611
2186561997
.
.
.
1125667899
The smallest possible number that can be framed is
1125667899 . 

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Diksha Singhal
Author: diksha1812


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