Watto, the owner of a spare parts store, has recently got an order for the mechanism that can process strings in a certain way. Initially the memory of the mechanism is filled with $*n*$ strings. Then the mechanism should be able to process queries of the following type: "Given string $*s*$, determine if the memory of the mechanism contains string $*t*$ that consists of the same number of characters as $*s*$ and differs from $*s*$ in exactly one position".

Watto has already compiled the mechanism, all that's left is to write a program for it and check it on the data consisting of $*n*$ initial lines and $*m*$ queries. He decided to entrust this job to you.

Input

The first line contains two non-negative numbers $*n*$ and $*m*$ ($0 ≤ *n* ≤ 3·10^{5}$, $0 ≤ *m* ≤ 3·10^{5}$) — the number of the initial strings and the number of queries, respectively.

Next follow $*n*$ non-empty strings that are uploaded to the memory of the mechanism.

Next follow $*m*$ non-empty strings that are the queries to the mechanism.

The total length of lines in the input doesn't exceed $6·10^{5}$. Each line consists only of letters 'a', 'b', 'c'.

Output

For each query print on a single line "YES" (without the quotes), if the memory of the mechanism contains the required string, otherwise print "NO" (without the quotes).