Given an array $A$ of $n$ integers and $q$ queries of either forms:
- `1 l r x`: increase each element $A_l,A_{l+1},...,A_r$ by $x$.
- `2 x`: find the maximum $j-i$ that $A_i=A_j=x$.
### Input
- The first line contains two integers $n,q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines, each line contains a query of the above forms.
### Output
- Print an integer, which is the answer for each query of type $2$. If there is no answer, print `-1`.
### Constraints
- $1 \le n,q \le 10^5$.
- $1 \le l, r \le n$.
- $1 \le A_i,x \le 2 \times 10^9$.
### Example
Input:
```
2 3
1 2
1 2 2 1
2 3
2 4
```
Output:
```
0
-1
```
