Note: This question is roughly similar to #C2022B, with only some differences in conditions and value ranges. These differences will affect the outcome.

Background

The background of the problem has no impact on solving it.

"Look, what is that?"

The Greenland is strolling in the deep starry sky. In the central command room, an elderly man with completely graying hair extended his wrinkled hand. In his hazy eyes, there was a light that had not flickered for an unknown amount of time.

Beside him was a woman as old as him. Upon hearing his words, the woman's body trembled as she tried to straighten up, but in the end, she collapsed onto the control chair. Her lips murmured, using a hoarse voice to produce one or two incomprehensible syllables.

She's too old. She is too old to do anything except live.

"The Aeon is up, the Aeon is up... Sally, we finally found it, did you see it?" A touch of yellow. In the distance, there is a faint purple nebula, but amidst the misty haze, there is a joyous and shimmering yellow.

"We, we gave everything, the Greenland we snatched from the Confederacy, and the 235 Gregorian years, 7 months, and 11 days we drifted in this universe..."

It can no longer be expressed in words. Even though women can no longer answer him with words. The man's rigid body seemed to burst out with infinite power, and he pounced on the console, precisely manipulating the dusty buttons one by one.

After finishing all of this, he suddenly leaned back on the control chair. Then, his gaze was fixed on that yellow, and now he just needed to wait patiently...

...

Nothing happened. The Greenland is still drifting slowly and steadily along its established route. Slowly, slowly move away from it.

The excitement is fading away.

"... Yes, yes. Sigh... but it still... came too late..."

He has become even more withered and old. His eyes have lost their light again, and it may never happen again in his lifetime.

"Two hundred years... we have been isolated from the world for two hundred years. We are already in order. Forever, we cannot escape..."

He couldn't remember what they had said two hundred years ago when the Greenland broke away from the Confederate fleet and was sealed in the invisible nest. For two hundred years, they have tried everything, and they have gone from taboo foreign love to wandering on the brink of death.

And it wasn't until they escaped from the invisible nest that they realized the rules of the Aeon had completely assimilated them, and they could no longer access the universe they were in.

Forever, forever.

That drop of yellow is still jumping with joy. Swinging. The Greenland continued to turn left, slid past it, and then flowed deeper into the invisible.

Description

The Greenland is wandering in the universe, with its only and ultimate goal being to find a touch of yellow - they call it 'Mortilin'. The regularized universe is an infinite $k$-dimensional space, and there are only whole points in the space. The coordinates of every point in the universe can be represented by a $k$-dimensional vector. Now the Greenland and Motilin are in two different coordinates, and they do not know each other's coordinates. At every moment, the Greenland can perform the following actions:

• Shuttle: Select a point with a Manhattan distance of $x$ from itself, and then move to this location. (Different from #C2022B where the Manhattan distance of the point from itself does not exceed $x$)
• Stay still.

And Motilin can only shuttle, with the same rules as the Greenland. The Greenland does not know what Mortilin will do, and Mortilin cannot possibly know about the actions of the Greenland. Assuming that the Greenland is smart enough to make the optimal choice every time, Mortilin will have a medium probability of choosing one from all possible actions, and the Greenland knows this. The Greenland wants to know if it can meet Mortilin at the same time and coordinate if time continues to pass.

Format

Input

The first line of input contains two integers $k$, $x$. The next two lines, each containing $k$ integers, represent the current coordinates of Greenland and Motilin in order.

Output

The output contains only one string. If they can meet, output Yes; otherwise, output No.

Samples

2 3
1 2
0 0

Yes

Range

For $50$% of the data, $k=1$;

For $100$% of the data, $1≤k≤50$, $1≤x≤4×10^7$, and the absolute value of each dimension of the coordinate vector shall not exceed $4×10^7$.

Hint

You say, will we see each other again?

Limitation

1s, 1024KiB for each test case.