Frog Traveler

Description:

Input:

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 300\,000$$$) — the depth of the well.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le i$$$), where $$$a_i$$$ is the maximum height Gorf can jump from $$$i$$$ meters below ground level.

The third line contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$0 \le b_i \le n - i$$$), where $$$b_i$$$ is the distance Gorf will slip down if he takes a break on $$$i$$$ meters below ground level.

Output:

If Gorf can't reach ground level, print $$$-1$$$. Otherwise, firstly print integer $$$k$$$ — the minimum possible number of jumps.

Then print the sequence $$$d_1,\,d_2,\,\ldots,\,d_k$$$ where $$$d_j$$$ is the depth Gorf'll reach after the $$$j$$$-th jump, but before he'll slip down during the break. Ground level is equal to $$$0$$$.

If there are multiple answers, print any of them.

Sample Input:

3
0 2 2
1 1 0

Sample Output:

2
1 0 

Sample Input:

2
1 1
1 0

Sample Output:

-1

Sample Input:

10
0 1 2 3 5 5 6 7 8 5
9 8 7 1 5 4 3 2 0 0

Sample Output:

3
9 4 0 

Note:

In the first example, Gorf is on the bottom of the well and jump to the height $$$1$$$ meter below ground level. After that he slip down by meter and stays on height $$$2$$$ meters below ground level. Now, from here, he can reach ground level in one jump.

In the second example, Gorf can jump to one meter below ground level, but will slip down back to the bottom of the well. That's why he can't reach ground level.

In the third example, Gorf can reach ground level only from the height $$$5$$$ meters below the ground level. And Gorf can reach this height using a series of jumps $$$10 \Rightarrow 9 \dashrightarrow 9 \Rightarrow 4 \dashrightarrow 5$$$ where $$$\Rightarrow$$$ is the jump and $$$\dashrightarrow$$$ is slipping during breaks.