Black-and-white field

You are tasked with creating a grid of size $n\times m$ ($1\le n,m\le 50$), where each cell is either white or black.

You are given two numbers, $a$ and $b$. The grid must contain exactly $a$ white components and $b$ black components.

A component of a specific color is defined as the largest group of adjacent cells of that color, where each cell in the group can be reached from any other cell in the same group by moving only through cells of the same color. Movement is allowed to adjacent cells that share a side (left, right, up, or down), but not diagonally.

Your task is to construct any grid of any size that contains exactly $a$ white components and $b$ black components.

Input

The first line contains two integers $a$ and $b$ ($1\le a,b\le 100$).

Output

Output two integers $n$ and $m$ ($1\le n,m\le 50$) representing the dimensions of the grid.

For each of the next $n$ rows, output $m$ numbers $c_{ij}$ ($0\le c_{ij}\le 1$), where $c_{ij}=0$ indicates a white cell and $c_{ij}=1$ indicates a black cell.

Examples

Scoring

Solutions that correctly handle cases where $a=b$ will receive at least $40$ points.

Solutions that correctly handle cases where $a=1$ will receive at least $20$ points.