Given two integer arrays $A$ and $B$ both of length $n$. You have to answer $q$ queries, each of the form $i, j$, determine if the set of elements (does not allow duplicity) formed from the prefix $A[1...i]$ and the set formed from prefix $B[1...j]$ are equal.
### Input
- The first line contains 2 integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The third line contains $n$ integeres $B_i$.
- The next $q$ lines, each line contains two integers $(i, j)$, a query.
### Output
- For each query, print `YES` if two sets are equal, otherwise print `NO`.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le A_i, B_i \le 10^9$.
- $1 \le i, j \le n$.
### Example
Input:
```
3 2
1 1 2
2 1 2
1 2
3 2
```
Output:
```
NO
YES
```
