There are $N$ stations on a certain line operated by AtCoder Railway. The $i$\-th station $(1 \leq i \leq N)$ from the starting station is named $S_i$.
Local trains stop at all stations, while express trains may not. Specifically, express trains stop at only $M \, (M \leq N)$ stations, and the $j$\-th stop $(1 \leq j \leq M)$ is the station named $T_j$.
Here, it is guaranteed that $T_1 = S_1$ and $T_M = S_N$, that is, express trains stop at both starting and terminal stations.
For each of the $N$ stations, determine whether express trains stop at that station.
## Input
Input is given from Standard Input in the following format:
$N$ $M$
$S_1$ $\ldots$ $S_N$
$T_1$ $\ldots$ $T_M$
## Constrains
* $2 \leq M \leq N \leq 10^5$
* $N$ and $M$ are integers.
* $S_i$ $(1 \leq i \leq N)$ is a string of length between $1$ and $10$ (inclusive) consisting of lowercase English letters.
* $S_i \neq S_j \, (i \neq j)$
* $T_1 = S_1$ and $T_M = S_N$.
* $(T_1, \dots, T_M)$ is obtained by removing zero or more strings from $(S_1, \dots, S_N)$ and lining up the remaining strings without changing the order.
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