Problem Statement

You are given integers $A,B$. You may perform the following operation on the integer $A$ up to $120$ times.

• Choose one positive divisor of $A$ and add it to $A$.

Input

$T$
$A_1\ B_1$
$A_2\ B_2$
$\vdots$
$A_T\ B_T$

Line $1$ contains the number of test cases $T$.
Each of the following $T$ lines contains integers $A_i,B_i$ separated by a space.

• All inputs are integers.
• $1 \le T \le 100$
• $1 \le A_i < B_i \le 10^{18}$

Output

Print $2T$ lines.
On line $2i - 1$, print the number of operations $K(1 \le K \le 120)$ for the $i$-th test case.
On line $2i$, print the integers $X_1 \ X_2 \dots X_K$ chosen in the operations for the $i$-th test case, separated by spaces.
$X_j$ is the integer added to $A_i$ in the $j$-th operation, and it must be a positive divisor of $A_i$ after the $j-1$-th operation.
Print a newline at the end.

Sample

2
26 57
100000000000 200000000000

4
1 9 2 19
1
100000000000