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).

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 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

见题面 Input 部分

见题面 Output 部分