Marisa has $n$ empty bottles arranged in a row. She will fill them up with several type of mushrooms.
She will perform $q$ operations. Each operation, she will either:
- Add a mushroom of type $x$ to each bottle in range $[l, r]$.
- Determine if all bottles in range $[l, r]$ have the same ingredients.
Help her answer the second operation!
### Input
- The first line contains two integers $n, q$.
- The next $q$ lines, each is a query of either form:
+ `1 l r x`: the first operation.
+ `2 l r`: the second operation.
### Output
- For each operation of type $2$, print `YES` if all bottles have the same ingredients, otherwise print `NO`.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le l \le r \le n$.
- $1 \le x \le 10^5$.
### Example
Input:
```
4 7
2 1 3
1 1 3 5
1 3 4 6
2 1 3
2 1 2
1 2 2 5
2 1 2
```
Output:
```
YES
NO
YES
NO
```
