Black-and-white field#10466

Black-and-white field

1 second
256 megabytes
Very easy

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

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

Input

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

Output

Output two integers and (1 \leq n, m \leq 50) — the dimensions of the grid.

For each of the next rows, output numbers c_{ij} (0 \leq c_{ij} \leq 1), where c_{ij}=0 indicates a white cell, otherwise — a black cell.

Examples

Example 1

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Example 2

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Scoring

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

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