Beautiful Number

Problem Description

You are given a number $X$ of length $n$, whose decimal digits are $a_1, a_2, \dots, a_n$ (ordered from left to right). You are also given an integer $k$.

You need to construct the smallest number $Y$ satisfying the following two conditions:

• For every position $i$ with $1 \le i \le m - k$, we have $b_i = b_{i+k}$;
• $X \le Y$,

where $b_1, b_2, \dots, b_m$ are the digits of $Y$ from left to right.

Input Format

The first line contains two integers $n, k$, where $2 \leq n \leq 200000$ and $1 \leq k < n$.

The second line contains $X$, written as a string of $n$ digits $a_1 a_2 \dots a_n$.

Output Format

The first line contains $m$, the length of $Y$.

The second line contains the smallest valid number $Y$, written as the digits $b_1 b_2 \dots b_m$.

Sample Input

3 2
353

Sample Output

3
353