Problem F. Ferryman of Hades ≡

Statement

"Ferryman of Hades" is a simple arcade game based on the Greek mythology. The main scene of the game is Styx river that is represented as a 1-dimensional line. Souls fall down from height H to this line. Charon must catch them in his boat when they touch the river line.

The boat of Charon is represented as a closed segment (containing its boundary points) of length L moving along line from the initial position [0, L].

Boat can move only from left to right with a fixed integer speed. It is known that i-th soul falls down to point P_i with a speed V_i.

A soul is caught if by the moment it crosses the river line, this point belongs to the boat.

Your program must, given H, L, P_i, and V_i, determine the minimum possible integer speed of the boat maximizing the number of caught souls.

Input format

Input contains integers H, L, and n, followed by n pairs of integers P_i, V_i.

Output format

Output must contain a single integer — the speed of the boat.

Constraints

0 < (H, L, V_i) ≤ 10⁶, 0 ≤ P_i ≤ 10⁶,

1 ≤ n ≤ 2 ⋅ 10⁵

Sample tests

10 2 4
2 1
3 8
4 7
5 8

2

10 2 4
9 3
8 2
6 3
8 2

0