Problem Statement

You are given an integer K. For a set S that is initially empty, process Q queries of the following two types in order:

• 1 x: An integer x is given. If x is in S, remove x from S. Otherwise, add x to S.
• 2 x: An integer x that is in S is given. Consider a graph where the vertices are the numbers in S, and there is an edge between two numbers if and only if the absolute difference between them is at most K. Print the count of vertices in the connected component that contains x.

Input

The input is given from Standard Input in the following format:
Q K
$\mathrm{query}_1$
$\vdots$
$\mathrm{query}_Q$

Each query is given in the following format:
1 x

2 x

Output

Process the queries.

Constraints

• $1 \leq Q \leq 2\times 10^5$
• $0 \leq K \leq 10^{18}$
• For each query, $1 \leq x \leq 10^{18}$.
• For each query of the second type, the given x is in S at that point.
• All input values are integers.

Sample Input 1

7 5
1 3
1 10
2 3
1 7
2 3
1 10
2 3

Sample Output 1

1
3
2

The query processing proceeds as follows:

• In the first query, 3 is added to S, resulting in S={3}.
• In the second query, 10 is added to S, resulting in S={3,10}.
• In the third query, consider a graph with vertices 3 and 10 and no edges. The connected component containing 3 has a size of 1, so print 1.
• In the fourth query, 7 is added to S, resulting in S={3,7,10}.
• In the fifth query, consider a graph with vertices 3, 7, and 10, with edges between 3 and 7, and 7 and 10. The connected component containing 3 has a size of 3, so print 3.
• In the sixth query, 10 is removed from S, resulting in S={3,7}.
• In the seventh query, consider a graph with vertices 3 and 7, with an edge between them. The connected component containing 3 has a size of 2, so print 2.

Sample Input 2

11 1000000000000000000
1 1
1 100
1 10000
1 1000000
1 100000000
1 10000000000
1 1000000000000
1 100000000000000
1 10000000000000000
1 1000000000000000000
2 1

Sample Output 2

10

Sample Input 3

8 0
1 1
1 2
2 1
1 1
1 2
1 1
1 2
2 1

Sample Output 3

1
1

见题面 Input 部分

见题面 Output 部分