The Hamming distance between two strings of bits (binary integers) is
the number of corresponding bit positions that differ. This can be
found by using XOR on corresponding bits or equivalently, by adding 
corresponding bits (base 2) without a carry. For example, in the two
bit strings that follow:

                               A      0 1 0 0 1 0 1 0 0 0
                               B      1 1 0 1 0 1 0 1 0 0
                            A XOR B = 1 0 0 1 1 1 1 1 0 0

The Hamming distance (H) between these 10-bit strings is 6, the number
of 1's in the XOR string.

Input  

There will be a sequence of instances.  For each instance, you
will be given a Hamming distance H and a bit string x.  The end
of the input will be indicated by a line with H=0.

Output  

For each instance, output
a list of all possible bit strings of length N that are Hamming
distance H from x, printed in lexicographic order.

Note:  If the length of x is N, the number of such bit strings is
N!/(H!(N-H)!).  The program should work for 1 <= H <= N <= 20. 

There should be a blank line between outputs for different instances.

Sample Input  

2 0000
1 000
0

Sample Output  

0011
0101
0110
1001
1010
1100

001
010
100