CF1601B.Frog Traveler

Frog Gorf is traveling through Swamp kingdom. Unfortunately, after a poor jump, he fell into a well of $n$ meters depth. Now Gorf is on the bottom of the well and has a long way up.

The surface of the well's walls vary in quality: somewhere they are slippery, but somewhere have convenient ledges. In other words, if Gorf is on $x$ meters below ground level, then in one jump he can go up on any integer distance from $0$ to $a_x$ meters inclusive. (Note that Gorf can't jump down, only up).

Unfortunately, Gorf has to take a break after each jump (including jump on $0$ meters). And after jumping up to position $x$ meters below ground level, he'll slip exactly $b_x$ meters down while resting.

Calculate the minimum number of jumps Gorf needs to reach ground level.

青蛙戈尔夫正在穿越沼泽王国。不幸的是，一次糟糕的跳跃后，他掉进了一口深度为 $n$ 米的井中。现在戈尔夫位于井底，需要向上爬很长一段距离。

井壁表面质量不均：有些地方很滑，而有些地方则有便于攀爬的凸起。换言之，若戈尔夫当前位于地下 $x$ 米处，则他单次跳跃最多可向上移动 $a_x$ 米，且可选择任意介于 $0$ 到 $a_x$（含端点）之间的整数米数。（注意：戈尔夫不能向下跳，只能向上跳。）

不幸的是，戈尔夫每次跳跃后（包括跳跃高度为 $0$ 米的情况）都必须休息。当他跳跃至地下 $x$ 米处并开始休息时，他会恰好向下滑落 $b_x$ 米。

请计算戈尔夫到达地面所需的最少跳跃次数。

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.

第一行包含一个整数 $n$（$1 \le n \le 300\,000$）—— 表示井的深度。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \le a_i \le i$），其中 $a_i$ 表示 Gorf 在地下 $i$ 米处所能跳跃的最大高度。

第三行包含 $n$ 个整数 $b_1, b_2, \ldots, b_n$（$0 \le b_i \le n - i$），其中 $b_i$ 表示 Gorf 在地下 $i$ 米处休息时将向下滑落的距离。

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.

如果戈尔夫无法到达地面，则输出 $-1$。否则，首先输出整数 $k$ —— 即最少可能的跳跃次数。

然后输出序列 $d_1,\,d_2,\,\ldots,\,d_k$，其中 $d_j$ 表示戈尔夫在第 $j$ 次跳跃后、但在休息期间向下滑落前所达到的深度。地面高度为 $0$。

若存在多个答案，输出任意一个即可。

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.

在第一个例子中，戈尔夫位于井底，跳跃后到达地面以下 $1$ 米的高度。随后他下滑 $1$ 米，停留在地面以下 $2$ 米的高度。此时，他只需一次跳跃即可到达地面。

在第二个例子中，戈尔夫可以跳跃至地面以下 $1$ 米处，但随后会滑回井底。因此他无法到达地面。

在第三个例子中，戈尔夫仅能从地面以下 $5$ 米的高度起跳到达地面。而戈尔夫可通过一系列跳跃达到该高度：$10 \Rightarrow 9 \dashrightarrow 9 \Rightarrow 4 \dashrightarrow 5$，其中 $\Rightarrow$ 表示跳跃，$\dashrightarrow$ 表示休息期间的下滑。