Score : $300$ points

Problem Statement

You are given positive integers $N$ and $M$. Find the maximum positive integer $X$ that satisfies all of the following conditions.

• $X$ is a positive integer less than $10^N$, and all digits in the decimal representation of $X$ are the same.
• $X$ is a multiple of $M$.

If no positive integer $X$ satisfies the conditions, print -1.

Constraints

• $1\leq N\leq 10^5$
• $1\leq M\leq 10^9$

Input

The input is given from Standard Input in the following format:

$N$ $M$

Output

Print the maximum positive integer $X$ that satisfies all of the conditions, or -1 if no such positive integer $X$ exists.

7 12

888888

Four positive integers $X$ satisfy the conditions: $444, 888, 444444, 888888$. The answer is the maximum of them, which is $888888$.

9 12

888888888

Six positive integers $X$ satisfy the conditions: $444, 888, 444444, 888888, 444444444, 888888888$.

1 3

9

Three positive integers $X$ satisfy the conditions: $3, 6, 9$.

1000 25

-1

No positive integers $X$ satisfy the conditions.

30 1

999999999999999999999999999999