Binary search turtle

from math import ceil
eps = 10 ** -5

vmax, d = map(int, input().split())
n = int(input())
x, t = [], []
for i in range(n):
    row = input().split()
    x.append( int(row[0]) )
    h, m = map(int, row[1].split(':'))
    t.append( h * 60 + m )

def float_equal(a, b):
    return abs(a - b) <= eps

def float_less(a, b):
    return a < b and not float_equal(a, b)

def float_less_or_equal(a, b):
    return float_equal(a, b) or float_less(a, b)

def time_to_last(wait_time):
    time = wait_time
    position = 0
    cnt_eat = 0
    for i in range(n):
        time += (x[i] - position) / vmax
        if not float_less(time, t[i]) and i < n - 1:
            cnt_eat += 1
            time += d
        position = x[i]
    return time, cnt_eat

left, right = 0, 10**9
while float_less(left, right):
    mid = (left + right) / 2
    tlast, cnt_eat = time_to_last(mid)
    if float_less_or_equal(tlast, t[-1]):
        left = mid
    else:
        right = mid

tlast, cnt_eat = time_to_last(right)
time = ceil(tlast + x[-1] / vmax + (n - cnt_eat) * d - eps)
print( "%02d:%02d" % ( time // 60, time % 60 ) )