Frog Traveler

题意翻译

### 题目描述 青蛙在 $n$ 米深的井中。 对于每一个深度，有两个量 $a_i$ 和 $b_i$。 $a_i$ 表示在深度为 $i$ 米的时候可以往上跳的最高高度，就是说在深度为 $i$ 米的地方可以往上跳 $\left[0,a_i\right]$ 米。 $b_i$ 表示在深度为 $i$ 米的地方时会往下滑 $b_i$ 米。 青蛙每跳一次，就会下滑一次。 请求出青蛙最少跳几次可以跳出井（深度为 $0$ 米）。 ### 输入格式 第一行输入一个正整数 $n$ 表示井的深度。 第 $2$ 行输入 $n$ 个整数，第 $i$ 个整数表示 $a_i$，含义见题目描述。 第 $3$ 行输入 $n$ 个整数，第 $i$ 个整数表示 $b_i$，含义见题目描述。 ### 输出格式 如果青蛙可以跳出井，输出 $2$ 行，第一行一个正整数表示跳的最少次数 $k$，第二行输出 $k$ 个整数表示跳 $k$ 次之后（下滑前）青蛙位于的深度。 如果青蛙跳不出井，输出 `-1`。 ### 数据范围 $1\le n\le3\times10^5,0\le a_i\le i,0\le b_i\le n-i$。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

3
0 2 2
1 1 0

输出样例 #1

2
1 0

输入样例 #2

2
1 1
1 0

输出样例 #2

-1

输入样例 #3

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

输出样例 #3

3
9 4 0

说明

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.