There is a 2D-plane where only lattice points with their x-coordinates from ~1~ to ~N~ are of interest.

Support the following operations:

• 1 n m b Add a line with an ID of ~n~ ~(1 \leq n \leq Q)~ in the form of ~y = mx + b~ to the plane. All line IDs are guaranteed to be distinct.
• 2 n Delete the line with an ID of ~n~. It is guaranteed that the line exists at this time.
• 3 c Output the ID of the line that gives the minimum value at ~x = c~ ~(c \in \mathbb{Z}, 1 \leq c \leq N)~. If multiple lines give the minimum value, output the ID of the line with a lower ID. It is guaranteed that there is least one line on the plane at this time.

You will be asked to support these operations a total of ~Q~ times.

Constraints

• ~1 \leq Q \leq 2 \cdot 10^5~
• ~1 \leq N \leq 10^9~
• ~0 \leq |m|, |b| \leq 10^8~

Input Specification

The first line of input will contain two numbers: ~N~ and ~Q~.

The next ~Q~ lines each contain an operation, as described above.

Output Specification

For each of the 3 c operation, output one line: the answer, as described above.

Sample Input

100 8
1 3 -10 2
1 1 -9 6
1 2 -4 4
1 4 1 1
3 39
2 4
2 3
3 40

Sample Output

3
1