Rikka with sequence

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)


As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Yuta have a sequence. Because the sequence is very self-willed(RenXing), at first the sequence is empty. And then Yuta do n operations on this sequence, each operation is either of these two types:

1.Add a number w into each gap of the sequence. For example if w=3 and the sequence before is “2 4”, it will be changed to “3 2 3 4 3”.
**after the first operation of the first type, there is only one number in the sequence**

2.Query the kth small number in the subsequence [L,R]. For example if k=2, L=2, R=4 and the sequence is “3 2 3 4 2”, the answer will be 3.

Yuta wants Rikka to tell him the answer of each query.

It is too difficult for Rikka. Can you help her?


The first line contains one number $n(n \leq 100000)$. Each of the following $n$ lines describes an operation: if it is “1 w” it will be the first type. Otherwise if it is “2 L R k”, it will be the second type. $(1 \leq w \leq 10^{9}, L \leq R \leq 10^{18})$
R will not be larger than the length of the sequence


For each query operation, output one number – the answer.

Sample Input

6 1 3 1 1 2 2 3 2 1 2 2 3 5 2 2 1 4 4

Sample Output

3 2 3




BestCoder Round #37 ($)