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). 

입력 형식

You may assume that 30 ≥ n > 0, 8 > k ≥ 0, and n ≥ 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.

출력 형식

예제 입력

3
2 1
2 0
4 2

예제 출력

The bit patterns are
10
01

The bit patterns are
00

The bit patterns are
1100
1010
1001
0110
0101
0011