CF1268A 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 $ .