1268A · Long Beautiful Integer

Problem: You are given an integer $x$ of $n$ digits $a_1, a_2, \ldots, a_n$, which make up its decimal notation in order from left to right.

Also, you are given a positive integer $k < n$.

Let's call integer $b_1, b_2, \ldots, b_m$ beautiful if $b_i = b_{i+k}$ for each $i$, such that $1 \leq i \leq m - k$.

You need to find the smallest beautiful integer $y$, such that $y \geq x$.

Input Format: The first line of input contains two integers $n, k$ ($2 \leq n \leq 200\,000, 1 \leq k < n$): the number of digits in $x$ and $k$.

The next line of input contains $n$ digits $a_1, a_2, \ldots, a_n$ ($a_1 \neq 0$, $0 \leq a_i \leq 9$): digits of $x$.

Output Format: In the first line print one integer $m$: the number of digits in $y$.

In the next line print $m$ digits $b_1, b_2, \ldots, b_m$ ($b_1 \neq 0$, $0 \leq b_i \leq 9$): digits of $y$.