Score : $200$ points

问题描述

Takahashi 正在一款电子游戏中探索一个洞穴。

该洞穴由 $N$ 个房间按一行排列。从入口开始，房间依次编号为 Room $1,2,\ldots,N$。

Takahashi 起初位于 Room $1$，并且有 时间限制 为 $T$。
对于每个 $1 \leq i \leq N-1$，他可以消耗时间为 $A_i$ 从第 $i$ 个房间移动到第 $(i+1)$ 个房间。这是在房间之间移动的唯一方式。他不能做出导致时间限制变为 $0$ 或更少的移动。

洞穴中有 $M$ 个奖励房间。第 $i$ 个奖励房间是 Room $X_i$；当他到达这个房间时，时间限制会增加 $Y_i$。

Takahashi 能否到达 Room $N$？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is exploring a cave in a video game.

The cave consists of $N$ rooms arranged in a row. The rooms are numbered Room $1,2,\ldots,N$ from the entrance.

Takahashi is initially in Room $1$, and the time limit is $T$.
For each $1 \leq i \leq N-1$, he may consume a time of $A_i$ to move from Room $i$ to Room $(i+1)$. There is no other way to move between rooms. He cannot make a move that makes the time limit $0$ or less.

There are $M$ bonus rooms in the cave. The $i$-th bonus room is Room $X_i$; when he arrives at the room, the time limit increases by $Y_i$.

Can Takahashi reach Room $N$?

Constraints

• $2 \leq N \leq 10^5$
• $0 \leq M \leq N-2$
• $1 \leq T \leq 10^9$
• $1 \leq A_i \leq 10^9$
• $1 < X_1 < \ldots < X_M < N$
• $1 \leq Y_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $T$

$A_1$ $A_2$ $\ldots$ $A_{N-1}$

$X_1$ $Y_1$

$X_2$ $Y_2$

$\vdots$

$X_M$ $Y_M$

Output

If Takahashi can reach Room $N$, print Yes; otherwise, print No.

Sample Input 1

4 1 10
5 7 5
2 10

Sample Output 1

Yes

• Takahashi is initially in Room $1$, and the time limit is $10$.
• He consumes a time of $5$ to move to Room $2$. Now the time limit is $5$. Then, the time limit increases by $10$; it is now $15$.
• He consumes a time of $7$ to move to Room $3$. Now the time limit is $8$.
• He consumes a time of $5$ to move to Room $4$. Now the time limit is $3$.

Sample Input 2

4 1 10
10 7 5
2 10

Sample Output 2

No

He cannot move from Room $1$ to Room $2$.

update @ 2024/3/10 11:11:35