Problem Statement

You are given positive integers $n, m$. Construct a $2 ^ n \times 2 ^ m$ matrix $A=(a_{i,j})_{1\leq i\leq 2^n,1\leq j\leq 2^m}$ satisfying all of the following conditions.

• Each integer at least $0$ and less than $2 ^ {n + m}$ appears in $A$ exactly $1$ time.
• For all integers $i,j,k,l$ such that $1\leq i\lt j \leq 2 ^ n, 1\leq k\lt l \leq 2 ^ m$, it holds that $a _ {i, k} \oplus a _ {i, l} \oplus a _ {j, k}\oplus a _ {j, l} = 0$. Here, $x\oplus y$ denotes the bitwise XOR of $x$ and $y$.

If no such $A$ exists, report that fact.

Input

The input is given from standard input in the following format.

$n\ m$

• All inputs are integers
• $1\leq n$
• $1\leq m$
• $n + m \leq 12$

Output

If an $A$ satisfying the conditions exists, on line $i\ (1\leq i\leq 2 ^ n)$ print $a _ {i, 1}, a _ {i, 2}, \ldots, a _ {i, 2 ^ m}$ in this order, separated by spaces. Print a newline after the last line as well. If there are multiple $A$ satisfying the conditions, you may print any of them.

If no $A$ satisfying the conditions exists, print -1 on line $1$, followed by a newline.

Sample

1 2

2 6 1 5
0 4 3 7