Thornhill Computer Club 2023 - September Contest - Problem 2

In the futuristic school of Zornhill Secondary School (ZSS), a magical classroom exists with a special property. This magical classroom has the ability to change its length and width by casting spells in order to accommodate any class size. The classroom can be divided into a grid of 1 x 1 meter squares which can each fit a single desk for each student. However, to increase personal space between students, desks cannot be within grid space away from each other in all directions (including diagonals). Mr. Z, a teacher of ZSS, has decided to use the classroom for his upcoming course but does not know how big the classroom must be to fit his ~N~ students.

To solve this, he decides to cast ~S~ spells to increase or decrease the width or length of the classroom.

Given that the classroom starts with an initial width of ~W~ and initial length of ~L~, can you determine whether the new classroom can fit all ~N~ students>?

Input Specifications

The first line of input will contain three integers, ~W~ and ~L~, the width and length of the classroom (~1 \le W, L \le 100~) and ~N~, the number of students in Mr. Z's class (~1 \le N \le 1000~).
The next line will contain a single integer ~S~ representing the number of spells Mr. Z cast (~0 \le S \le 100~).
The next ~S~ lines will contain two integers, ~C_w~ and ~C_l~ representing the change in width and the change in length of the ~S_th~ spell (~-100 \le C_w, C_l \le 100~).
Due to limitations with magic, if spells are casted to decrease the size of the classroom below 1 x 1, the classroom would continue to shrink until it reaches a size of 1 x 1.

Output Specifications

Output yes or no depending on whether or not the new class is large enough to fit Mr. Z's ~N~ students.

Sample Input 1

3 3 10
5
-2 1
6 -2
-3 5
5 -3
-1 1

Sample Output 1

yes

Explanation for Sample Output 1

After 5 spells, the final classroom size will be 8 x 5. In a class of this size, 10 desks for 10 students can fit inside this classroom in the following configuration.

Sample Input 2

10 8 1000
3
23 5
12 36
9 23

Sample Output 2

no

Explanation for Sample Output 2

The final room size would be 54 x 72 spaces. It is impossible to fit 1000 desks into a room of this size without having all desks at least one grid space away from each other.

Sample Input 3

10 10 5
8
95 34
12 1
-96 45
34 21
-23 -87
-64 -51
17 35
-15 -31

Sample Output 3

yes