Problem9595--ABC245 —— C - Choose Elements

9595: ABC245 —— C - Choose Elements

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

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 $i(1\leq i\leq N-1)$.

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`.

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.

Sample 1 Input

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

Sample 1 Output

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

Sample 2 Input

4 90
1 1 1 100
1 2 3 100

Sample 2 Output

No
No X satisfies all conditions.

Sample 3 Input

4 1000000000
1 1 1000000000 1000000000
1 1000000000 1 1000000000

Sample 3 Output

Yes

Source/Category