Score : $300$ points

Problem Statement

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.

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.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$S_1$ $\ldots$ $S_N$

$T_1$ $\ldots$ $T_M$

Output

Print $N$ lines. The $i$-th line $(1 \leq i \leq N)$ should contain Yes if express trains stop at the $i$-th station from the starting station, and No otherwise.

5 3
tokyo kanda akiba okachi ueno
tokyo akiba ueno

Yes
No
Yes
No
Yes

7 7
a t c o d e r
a t c o d e r

Yes
Yes
Yes
Yes
Yes
Yes
Yes

Express trains may stop at all stations.