Om Nom and Necklace

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，$1\leq i\leq n$），如果满足 $\texttt{ABABA...BA}$ 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。

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. 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.

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.

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.

7 2
bcabcab

0000011

21 2
ababaababaababaababaa

000110000111111000011

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".