A. Long Beautiful Integertime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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. InputThe 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.OutputIn 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.ExamplesInput
3 2
353
Output
3
353
Input
4 2
1234
Output
4
1313

3 2
353

3 353 
['constructive algorithms', 'greedy', 'implementation', 'strings', '*1700']