Explore

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 $2$.