## 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.

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'

Time Limit: 2.5 Seconds
Memory Limit: 256MB