pigeonhole

Problem Description

The pigeonhole principle states that given n+1 pigeons and n holes and that all pigeons are put into a hole, there must exist some hole that contains at least 2 pigeons.

More generally, given p pigeons and n holes, there must exist some hole with ceil(p/n) pigeons.

Guan is not convinced and wants to run a program to prove this.

Each run of the program will simulate p pigeons leaving or entering holes. There will be h holes, numbered from 0 to h-1.

Each pigeon has a number pi and will enter the hole (pi mod h) (i.e. pi%h) when it enters.

Two pigeons may not have the same number.

You are required to output whether there exist two pigeons in the same hole.

Input

The first line of the input contains two integers, the number of operations n, and the number of holes h.

For the next n lines, each line consists of an integer, either 0 or 1, 1 indicating entry and 0 indicating leaving of a pigeon. This integer is followed by another integer pi, indicating the number of the pigeon entering/leaving.

No pigeon will leave before it has entered.

Constraints

1<=pi<=1,000,000,000

Output

For each operation, output an integer on each line, the maximum number of pigeons in one hole.

Subtasks

Subtask 1 (30%) n,h<=2000

Subtask 2 (70%) n,h<=2000000

Sample Testcase 1

Input

5 3
1 1
1 9001
0 9001
1 2
0 2
Output
1
2
1
1
1

Explanation

Pigeon 9001 shares the same hole as pigeon 1 (hole 1) (9001%3=1), but pigeon 2 does not share the same hole as pigeon 1, hence after operation two, there are two pigeons in the same hole, but not after operation three.

Sample Testcase 2

Input

5 3
1 1
1 9001
1 2
0 2
0 9001
Output
1
2
2
2
1


Submitting .cpp to 'pigeonhole'


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Compile Errors


							
Time Limit: 2.5 Seconds
Memory Limit: 256MB
No. of ACs: 57
Your best score: 0
Source: Dunjudge Archive

Subtask Score
1 30
2 70
3 0