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 ~0 < n \le 30~, ~0 \le k < 8~, and ~k \le n~. 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