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