Scenery

Images by John Fowler, Carol Highsmith, and Richard Woodland

You spend one day of a trip to Rapid City photographing the South Dakota Badlands, a place known for its unusual land formations. You are an amateur photographer and very particular about light, so you picked one spot with a wide view and listed $n$ features you want to photograph from it.

Feature $i$ only looks the way you want while the sun sits in the right range of positions. You may start that photograph no earlier than time $a_i$, and it must be finished by time $b_i$. Repositioning the tripod and the camera takes a while, so every photograph takes exactly $t$ units of time. You photograph one feature at a time and never interrupt a photograph once it has started, so a photograph begun at time $s$ occupies the whole interval from $s$ to $s + t$.

Decide whether you can photograph all $n$ features in one day.

The first line contains two integers $n$ and $t$ ($1 \le n \le 10^4$, $1 \le t \le 10^5$), where $n$ is the number of photographs you want and $t$ is the time one photograph takes.

Each of the next $n$ lines describes the time window of one photograph with two integers $a$ and $b$ ($0 \le a$, $a + t \le b \le 10^9$). You may begin that photograph no earlier than $a$, and it must be finished by $b$.

Print yes if all $n$ photographs can be taken, and no otherwise.