XY

Kaloyan was preparing an exam for his students and found the following problem to be pretty interesting. He wrote two numbers $X$ and $Y$ and wants to find a sequence of integers where the sum of every $X$ consecutive elements (in the sequence) is strictly positive while the sum of every $Y$ consecutive elements is strictly negative.

Kaloyan found out that this sequence cannot be infinitely long. He tried to find a sequence of maximum possible length with the described property. However, it turns out to be rather difficult problem for Kaloyan. Help him by writing a program XY that finds the maximum length of such a sequence. You should find the answers to $Q$ such pairs $X$ and $Y$. Additionally, you have to find a maximal sequence only for the first query.

The only line of the standard input contains one number $Q$ - the number of queries. Each of the following $Q$ lines contains two numbers - $X$ and $Y$ .

On the first line of the standard output you should print $Q$ numbers - $N_1, N_2, \dots, N_Q$, separated with intervals, where $N_i$ is the answer for the $i^{th}$ query. On the second line you should print $N_1$ integers separated with intervals - a sequence with the desired property for the first query.

• $1 \leq X,Y \leq 100\ 000$
• $1 \leq Q \leq 100\ 000$