Ostad thinks that the usual way of factoring numbers is too mathematical, so he invented a new notion called XOR-factorization, which is more computer-science-like. For a given integer $$$n$$$, a sequence of integers $$$a_1, a_2, \ldots, a_k$$$ with $$$0 \le a_i \le n$$$ for all $$$i$$$ is called a XOR-factorization of $$$n$$$ if and only if $$$$$$ a_1 \oplus a_2 \oplus \cdots \oplus a_k = n, $$$$$$ where $$$\oplus$$$ denotes the bitwise XOR operation.

You are given integers $$$n$$$ and $$$k$$$. Find a XOR-factorization $$$a_1, a_2, \ldots, a_k$$$ of $$$n$$$ that maximizes the sum $$$a_1 + a_2 + \cdots + a_k$$$.

It can be proven that under the problem conditions, a XOR-factorization always exists.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

Each of the next $$$t$$$ lines contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^9$$$, $$$1 \le k \le 10^5$$$).

It is guaranteed that the sum of $$$k$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output $$$k$$$ integers $$$a_1, a_2, \ldots, a_k$$$ such that $$$0 \le a_i \le n$$$.

We can show that an answer always exists. If there are multiple valid answers, you may print any of them in any order.

Note

In the first test case, we can factor $$$5$$$ as $$$1 \oplus 4 \oplus 5 \oplus 5$$$ with a sum of $$$15$$$, and it can be shown that no other XOR-factorization has a higher sum.

In the second test case, we can factor $$$4$$$ as $$$4 \oplus 4 \oplus 4$$$ with a sum of $$$12$$$, which is trivially the maximum possible.

XOR-factorization

Examples