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Contest: Task: Related: TaskB TaskD

Score : $300$ points

Problem Statement

You are given two sequences, each of length $N$, consisting of integers: $A=(A_1, \ldots, A_N)$ and $B=(B_1, \ldots, B_N)$.

Determine whether there is a sequence of length $N$, $X=(X_1, \ldots, X_N)$, satisfying all of the conditions below.

  • $X_i = A_i$ or $X_i = B_i$, for every $i(1\leq i\leq N)$.

  • $|X_i - X_{i+1}| \leq K$, for every $i(1\leq i\leq N-1)$.

Constraints

  • $1 \leq N \leq 2\times 10^5$
  • $0 \leq K \leq 10^9$
  • $1 \leq A_i,B_i \leq 10^9$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$
$A_1$ $\ldots$ $A_N$
$B_1$ $\ldots$ $B_N$

Output

If there is an $X$ that satisfies all of the conditions, print Yes; otherwise, print No.

Sample Input 1

5 4
9 8 3 7 2
1 6 2 9 5

Sample Output 1

Yes

$X=(9,6,3,7,5)$ satisfies all conditions.

Sample Input 2

4 90
1 1 1 100
1 2 3 100

Sample Output 2

No

No $X$ satisfies all conditions.

Sample Input 3

4 1000000000
1 1 1000000000 1000000000
1 1000000000 1 1000000000

Sample Output 3

Yes