UVa 729 the Hamming Distance Problem: Full array output and small details

729-the Hamming Distance Problem

Time limit:3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=670

The Hamming distance between two strings of bits (binary integers) is the number of corresponding bit positions that Diffe R. This can is found by using XOR on corresponding bits or equivalently and by adding corresponding bits (base 2) without a C Arry. 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

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

Input

Input consists of several datasets. The "a" of the input contains the number of datasets, and it's followed by a blank line. Each dataset is contains N, the length of the bit strings and H, the Hamming distance, on the same line. There is a blank line between test cases.

Output

For each dataset print a list of all possible bit strings of length N so are Hamming distance H from the bit string cont Aining all 0 ' s (Origin). This is, the all bit strings of the length N with exactly H 1' s printed in ascending lexicographical order.

The number of such bit strings is equal to the combinatorial symbol C(N,H). This is the number of possible combinations of N-H Zeros and H ones. It is equal to

This number can be very large. The program should work for

.

Print a blank line between datasets.

Sample Input

1

4 2

Sample Output

0011
0101
0110
1001
1010
1100

Add empty characters Ah ...