Score : $300$ points

问题描述

给定两个长度均为 $N$ 的整数序列：$A=(A_1, \ldots, A_N)$ 和 $B=(B_1, \ldots, B_N)$。

确定是否存在一个长度为 $N$ 的序列 $X=(X_1, \ldots, X_N)$，满足以下所有条件：

• 对于每个 $i(1\leq i\leq N)$，有 $X_i = A_i$ 或者 $X_i = B_i$。

• 对于每个 $i(1\leq i\leq N-1)$，满足 $|X_i - X_{i+1}| \leq K$。

以上为通义千问 qwen-max 翻译，仅供参考。

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

update @ 2024/3/10 10:31:15