Bru and the Orange Split

Bru has a warehouse with $10^9$ oranges of each taste from $1$ to $10^9$. Bru wants to share the oranges with friends.

Bru will invite a total of $N$ friends. The value of $N$ is not yet fixed. The $N$ friends stand in a line and each takes one orange from Bru. Bru wants to give out the oranges so that the following conditions hold.

Let the friends be numbered $1$, $2$, $\cdots$, $N$ in the order they arrive. Let $A_i$ be the taste of the orange given to friend $i$. Then,

• The number of pairs $(i, j)$ with $i<j$ and $A_i < A_j$ is $X$.
• The number of pairs $(i, j)$ with $i<j$ and $A_i > A_j$ is $Y$.

If several ways satisfy these conditions, Bru wants to save oranges and picks the way with the smallest $N$. Write a program that invites friends and gives out oranges so that Bru's conditions are met.

The first line contains two integers $X$ and $Y$, separated by a space.

The first line prints the number of friends $N$.

The second line prints the tastes $A_1, A_2, \cdots, A_N$ of the oranges given to the $N$ friends, separated by spaces.

If several ways are possible, print a way with the smallest $N$. If there are still several such ways, print any of them.

It is guaranteed that a valid way with $N \le 10^6$ always exists.

• $0 \le X, Y \le 10^9$
• $X + Y > 0$
• Each element of $A$ is an integer from $1$ to $10^9$.