B. Digits
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Artem wrote the digit $$$d$$$ on the board exactly $$$n!$$$ times in a row. So, he got the number $$$dddddd \dots ddd$$$ (exactly $$$n!$$$ digits).

Now he is curious about which odd digits from $$$1$$$ to $$$9$$$ divide the number written on the board.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The next $$$t$$$ test cases follow.

Each test case consists of a single line containing two integers $$$n$$$ and $$$d$$$ ($$$2 \le n \le 10^9$$$, $$$1 \le d \le 9$$$).

Output

For each test case, output the odd digits in ascending order that divide the number written on the board.

Example
Input
3
2 6
7 1
8 5
Output
1 3 
1 3 7 9 
1 3 5 7 9
Note

The factorial of a positive integer $$$n$$$ ($$$n!$$$) is the product of all integers from $$$1$$$ to $$$n$$$. For example, the factorial of $$$5$$$ is $$$1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120$$$.