Problem Description

Given you two integers $N$,$K$,you need to construct a set of $N$-dimensional vectors of size $N$.Each dimension of each vector can only be $0$ or $1$. And for a vector, its sum of all dimensions is $K$. Meanwhile, any vector can't be represented by other vectors using $XOR$ operation.

If such a vector group exists, find the minimum vector group, otherwise output $-1$. (Define the minimum set of vectors as the minimum lexicographic order after each vector is converted to binary)

Input

There are $T(1 \leq T \leq 1000)$ test cases in this problem.

For every test case,the first line has two integer $N(1 \leq N \leq 62)$,$K(1 \leq K \leq N)$.

Output

If the vector group does not exist, output $-1$.

Otherwise output the minimum vector group, expressed in decimal notation.

2
5 3
5 1

7 11 13 14 19
1 2 4 8 16