Codeforces Round 1133 (Div. 1, Div. 2) is coming soon! Register here. ×
C2. Disgusting + GCD (Checker Version)
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

In this version, you need to implement part of the checker for the constructive version.

In this version, you are ogiyo.

kijjot gives you two integers $$$a$$$ and $$$b$$$ such that $$$a \le b$$$. In one operation, you can choose a positive integer $$$x$$$ such that $$$\gcd(a, x) = 1$$$$$$^{\text{∗}}$$$, and then increase $$$a$$$ by $$$x$$$.

Your task is to find any sequence of operations of the minimum possible length to transform $$$a$$$ into $$$b$$$. It can be shown that under the given constraints, it is always possible to transform $$$a$$$ into $$$b$$$ using at most $$$15$$$ operations.

$$$^{\text{∗}}$$$$$$\gcd(x, y)$$$ denotes the greatest common divisor (GCD) of integers $$$x$$$ and $$$y$$$.

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 test case contains two integers $$$a$$$ and $$$b$$$ ($$$2 \le a \le 10^5$$$, $$$a \le b \le 10^9$$$) — the numbers given to you by kijjot.

Output

For each test case, output the minimum number of operations $$$k$$$ ($$$0 \le k \le 15$$$) in the first line.

In the second line, output $$$k$$$ positive integers $$$x_1, x_2, \ldots, x_k$$$ — the values of $$$x$$$ chosen in the operations, in order. These operations must be valid and transform $$$a$$$ into $$$b$$$.

If $$$k = 0$$$, you may omit the second line. If there are multiple optimal sequences, output any of them.

Example
Input
4
2 2
15 25
2184 2200
100000 1000000000
Output
0
2
1 9
3
11 2 3
2
1636673 998263327
Note

In the first test case, $$$a = b = 2$$$, so no operations are needed.

In the second test case, we can first add $$$1$$$ to obtain $$$16$$$, and then add $$$9$$$ to obtain $$$25$$$. Both operations are valid because $$$\gcd(15, 1) = 1$$$ and $$$\gcd(16, 9) = 1$$$. It can be shown that fewer than $$$2$$$ operations are not enough.