A13149. Long Beautiful Integer

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 $y \geq x$ .

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 $x$ .

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 $y$ .