### ** 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 **p**_{i} and will enter the hole **(p**_{i} mod h) (i.e. p_{i}%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 p_{i}, indicating the number of the pigeon entering/leaving.

No pigeon will leave before it has entered.

## Constraints

1<=p_{i}<=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