# Problem D

Buried Treasure

Buried treasure can be found using treasure maps. There are $m$ different locations numbered from $1$ to $m$. Each location contains either treasure or a trap.

Joey gives you $n$ treasure maps. Each treasure map has two markers $m_1, m_2$. For $i\in \{ 1,2\} $, if $m_ i < 0$, then the map is claiming that location $|m_ i|$ contains a trap. If $m_ i > 0$, then the map is claiming that location $|m_ i|$ contains treasure.

We say that a treasure map is *reasonable* if at least one of the claims it makes
is correct. For example, if a map claims that location
$1$ contains treasure and
location $2$ contains a
trap, while in reality location $1$ contains a trap and location
$2$ contains treasure,
then the map is *not* reasonable.

Joey asserts that every treasure map that he has given you is reasonable. Can you check whether this is possible, i.e. whether there exists an assignment of locations $1$ through $m$ to either treasure or trap such that each map makes at least one correct claim?

## Input

The first line of input contains two space-separated integers $n$, the number of treasure maps you have, and $m$, the number of possible locations on the treasure maps ($1 \leq n \leq 10^{5}, 1 \leq m \leq 10^{5}$).

The next $n$ lines of input each contain $2$ integers. For $1\leq j \leq n$, the $j^{th}$ line contains two integers $m_1, m_2$ ($-m \leq m_1, m_2 \leq m$, and $m_1, m_2 \neq 0$) which represent the two locations marked by map $j$.

## Output

If itâ€™s possible for every map to be reasonable, print YES. Otherwise, print NO.

## Sample Explanation

In Sample Input $1$, there is no assignment of locations to either treasure or trap to make all maps reasonable. If for example we say that location $1$ and $2$ both contain treasure, then map $4$ will not be reasonable, while if we say that location $1$ contains a trap and location $2$ contains treasure, then map $3$ will not be reasonable. The other cases are similar.

In Sample Input $2$, if location $1$ contains a trap and location $2$ contains treasure, then all $3$ maps will be reasonable.

Sample Input 1 | Sample Output 1 |
---|---|

4 2 1 2 2 -1 1 -2 -1 -2 |
NO |

Sample Input 2 | Sample Output 2 |
---|---|

3 2 1 2 2 -1 -1 -2 |
YES |