Om Nom and Necklace

题意翻译

已知长度为n的字符串s,对于s的每一个前缀子串(即对于每一个i,s中从第1个字符到第i个的所有字符组成的字符串,1<=i<=n),如果满足ABABA...BA的形式(A、B可以为空,也可以是一个字符串,A有k+1个,B有k个),则请输出1,否则输出0,注意:n和k给定。

题目描述

One day Om Nom found a thread with $ n $ beads of different colors. He decided to cut the first several beads from this thread to make a bead necklace and present it to his girlfriend Om Nelly. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF526D/76315fd43cfbe5e147469d75b9c643c18f6f5673.png)Om Nom knows that his girlfriend loves beautiful patterns. That's why he wants the beads on the necklace to form a regular pattern. A sequence of beads $ S $ is regular if it can be represented as $ S=A+B+A+B+A+...+A+B+A $ , where $ A $ and $ B $ are some bead sequences, " $ + $ " is the concatenation of sequences, there are exactly $ 2k+1 $ summands in this sum, among which there are $ k+1 $ " $ A $ " summands and $ k $ " $ B $ " summands that follow in alternating order. Om Nelly knows that her friend is an eager mathematician, so she doesn't mind if $ A $ or $ B $ is an empty sequence. Help Om Nom determine in which ways he can cut off the first several beads from the found thread (at least one; probably, all) so that they form a regular pattern. When Om Nom cuts off the beads, he doesn't change their order.

输入输出格式

输入格式


The first line contains two integers $ n $ , $ k $ ( $ 1<=n,k<=1000000 $ ) — the number of beads on the thread that Om Nom found and number $ k $ from the definition of the regular sequence above. The second line contains the sequence of $ n $ lowercase Latin letters that represent the colors of the beads. Each color corresponds to a single letter.

输出格式


Print a string consisting of $ n $ zeroes and ones. Position $ i $ ( $ 1<=i<=n $ ) must contain either number one if the first $ i $ beads on the thread form a regular sequence, or a zero otherwise.

输入输出样例

输入样例 #1

7 2
bcabcab

输出样例 #1

0000011

输入样例 #2

21 2
ababaababaababaababaa

输出样例 #2

000110000111111000011

说明

In the first sample test a regular sequence is both a sequence of the first 6 beads (we can take $ A= $ "", $ B= $ "bca"), and a sequence of the first 7 beads (we can take $ A= $ "b", $ B= $ "ca"). In the second sample test, for example, a sequence of the first 13 beads is regular, if we take $ A= $ "aba", $ B= $ "ba".