CCC '96 S3 - Pattern Generator

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Points: 5
Time limit: 2.0s
Memory limit: 16M

Problem type

Write a program that repeatedly reads two numbers n and k and prints all bit patterns of length n with k ones in descending order (when the bit patterns are considered as binary numbers). You may assume that 30 \ge n > 0, 8 > k \ge 0, and n \ge k. The first number in the input gives the number of pairs n and k. The numbers n and k are separated by a single space. Leading zeroes in a bit pattern should be included. See the example below.

Sample Input

3
2 1
2 0
4 2

Sample Output

The bit patterns are
10
01

The bit patterns are
00

The bit patterns are
1100
1010
1001
0110
0101
0011

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