Given $n$ strings $S_1, S_2, ..., S_n$. There are $q$ queries, each consisting of two integers $x, y$. Check whether $S_x$ is a substring (not necessarily contiguous) of $S_y$ or if $S_y$ is a substring (not necessarily contiguous) of $S_x$.
### Input
- The first line contains two integers $n, q$.
- The next $n$ lines, where the $i$-th line represents the string $S_i$.
- The next $q$ lines, each containing two integers $x, y$.
### Output
- For each query, print `YES` if $S_x$ is a substring of $S_y$ or if $S_y$ is a substring of $S_x$, otherwise print `NO`.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le \sum |S_i| \le 10^6$
- $1 \le x, y \le n$.
- All strings consist only of lowercase letters.
### Example
Input:
```
3 3
aab
db
dacb
2 1
2 3
1 3
```
Output:
```
NO
YES
NO
```
