Problem Statement

The battery of Takahashi's smartphone has N mAh capacity. At time 0.5, 1.5, 2.5, and so on (that is, at time n + 0.5 for every integer n), the battery charge decreases by 1 mAh.
Takahashi will leave his house with his phone fully charged at time 0, visit a cafe M times, and return home at time T.
He will stay at the i-th cafe from time A_i to time B_i. During this stay, he charges his phone, so the battery charge does not decrease. Instead, at time n + 0.5 for every integer n, it increases by 1. However, if it is already equal to the battery capacity, it does not increase nor decrease.
Determine whether he can return home without the battery charge dropping to 0 on the way.

Input

Input is given from Standard Input in the following format:
N M T
A_1 B_1
A_2 B_2
A_3 B_3
$\hspace{15pt} \vdots$
A_M B_M

Output

If Takahashi can return home without the battery charge dropping to 0 on the way, print Yes; otherwise, print No.

Constraints

• $1 \le N \le 10^9$
• $1 \le M \le 1000$
• $1 \le T \le 10^9$
• $0 \lt A_1 \lt B_1 \lt A_2 \lt B_2 \lt A_3 \lt B_3 \lt \dots \lt A_M \lt B_M \lt T$
• All values in input are integers.

Sample Input 1

10 2 20
9 11
13 17

Sample Output 1

Yes

The battery charge changes as follows:

• Time 0 (leaving home): 10 mAh
• Time 9 (the beginning of the stay at the first cafe): 1 mAh
• Time 11 (the end of the stay at the first cafe): 3 mAh (He charges his phone in a cafe.)
• Time 13 (the beginning of the stay at the second cafe): 1 mAh
• Time 17 (the end of the stay at the second cafe): 5 mAh
• Time 20 (getting home): 2 mAh

During this process, the battery charge never drops to 0, so we print Yes.

Sample Input 2

10 2 20
9 11
13 16

Sample Output 2

No

This case is the same as Sample Input/Output 1 until he starts his stay at the second cafe with 1 mAh charge.
When he ends his stay there at time 16, the battery charge is 4 mAh.
Then at time 19.5, it drops to 0, so we print No.

Sample Input 3

15 3 30
5 8
15 17
24 27

Sample Output 3

Yes

The battery charge drops to 1 mAh when he gets home, but it never drops to 0 on the way.

Sample Input 4

20 1 30
20 29

Sample Output 4

No

The battery charge drops to 0 at time 19.5.

Sample Input 5

20 1 30
1 10

Sample Output 5

No

Note that when the battery charge is equal to the battery capacity, staying at a cafe does not increase the battery charge.

见题面 Input 部分

见题面 Output 部分