Building Blocks

Ignas has three kinds of building blocks. Blocks of each kind have a different color and a different height. Luckily for Ignas, he has an unlimited supply of each kind.

Ignas wants to use these blocks to build a tower exactly $N$ centimeters tall. However, he wants the tower to be a single color, so he may use blocks of only one kind.

It may be impossible to build a tower of exactly $N$ centimeters from a single kind of block. For example, if a block is $3$ cm tall, he can build towers of $3$ cm, $6$ cm, or $9$ cm, but not towers of $7$ cm or $10$ cm.

Ignas wants to choose the kind of block that lets him build a tower whose height is as close to $N$ as possible. The tower must contain at least one block (a tower of height $0$ is not allowed). Help Ignas pick the most suitable blocks.

The first line contains the desired tower height $N$ (in centimeters). The second line contains three distinct integers $a$, $b$, and $c$: the heights (in centimeters) of the three kinds of blocks.

Print two integers: the height of the block Ignas should choose, and the height of the tower (closest to $N$) that he can build from it.

• If a single kind of block can build two towers equally close to $N$, choose the shorter tower (the smaller multiple).
• If several kinds of block achieve the same minimal distance to $N$, choose the block with the smaller height.

• $1 \le N \le 1000$
• $1 \le a < b < c \le 100$