dynamic_programming1.py

from functools import lru_cache


@lru_cache(maxsize=None)
def calculate_probability_recursively(red, green):
    if green == 0 or red == 0:
        return 1

    p0 = red / (red + green)
    if green == 1:
        return p0

    return p0 + green / (red + green) * (green - 1) / (red + green - 1) * calculate_probability(red, green-2)


def calculate_probability(red, green):
    if green == 0 or red == 0:
        return 1
    if green == 1:
        return red / (red + green)

    queue = [(red, green)]
    while queue:
        if green > 1:
            green -= 2
            queue.append((red, green))
        else:
            r, g = queue.pop()
            if g == 0:
                dp = 1
            elif g == 1:
                dp = r / (r + g)
            else:
                p = r / (r + g) + g / (r + g) * (g - 1) / (r + g - 1) * dp
                dp = p
    return p


T = int(input().strip())

for _ in range(T):
    red, green = [int(el) for el in input().split(' ')]
    value = calculate_probability(red, green)
    print("%8.6f" % value)