In the language of a certain country, there are $n$ words. A sentence in this language must be represented by concatenating some words from this language, and a word can be used multiple times. For example, if the language has three words `ma`, `ri`, `sa`, then `marisa` is a valid sentence, `ririri` is also valid, but `maris` is not.
Given $q$ queries, each query is a string $S$, check whether this string is a valid sentence in this language or not.
### Input
- The first line consists of two integers $n, q$.
- The next $n$ lines, each line is a word in this language.
- The next $q$ lines, each line is a string $S$, a query.
### Output
- For each query, print `YES` on a separate line if the string is a valid sentence in this language; otherwise, print `NO`.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le \sum{|S|} \le 10^5$.
- All strings consist only of lowercase letters. The length of each word in this language does not exceed $10$.
### Example
Input:
```
3 5
ma
ri
sa
marisa
sarima
rias
mamasa
ririririma
```
Output:
```
YES
YES
NO
YES
YES
```
