Task

Return a list of all numbers that have no more than n bits, such that exactly k of them are set to 1.

Input/Output

[input] integer n

The maximum number of bits the number can have.

1 ≤ n ≤ 20.

[input] integer k

The number of bits equal to 1.

0 ≤ k ≤ 20.

[output] an integer array

The numbers with at most n bits k of which are set to 1 sorted in ascending order.

Example

For n = 4 and k = 1, the output should be [1,2,4,8].

1₁₀ = 1₂, which obviously has 1 number of bits, and the only bit is 1.

2₁₀ = 10₂, which has 2 number of bits, with the first one equal to 1.

4₁₀ = 100₂, which has 3 number of bits, with the first one equal to 1.

8₁₀ = 1000₂, which has 4 number of bits, with the first one equal to 1.

For n = 5 and k = 5, the output should be [31].

31₁₀ = 11111₂, which exactly has 5 bits qualt to 1.

For n = 3 and k = 20, the output should be [].

No such a number that has not greater 3 bits and exactly has 20 bits qualt to 1.

For n = 20 and k = 0, the output should be [0].

0₁₀ = 0₂, which exactly has 0 bits qualt to 1.