crt.py

from decimal import Decimal, getcontext
getcontext().prec = 500
# copied from some site
def bezout(a, b):
    # Apply the Extended Euclidean Algorithm
    u1, v1, r1 = 1, 0, a
    u2, v2, r2 = 0, 1, b

    while r2:
        q = r1 // r2
        u1, u2 = u2, u1-q*u2
        v1, v2 = v2, v1-q*v2
        r1, r2 = r2, r1-q*r2
        assert u1*a + v1*b == r1
        assert u2*a + v2*b == r2

    if r1 < 0:
        u1, v1, r1 = -u1, -v1, -r1

    return (u1, v1, r1)

def crt(cong1, cong2):
    # Apply the Chinese Remainder Theorem
    a1, n1 = cong1
    a2, n2 = cong2
    c1, c2, g = bezout(n1, n2)
    assert n1*c1 + n2*c2 == g

    if (a1 - a2) % g != 0:
        raise ValueError(f"Incompatible congruences {cong1} and {cong2}.")

    lcm = n1 // g * n2
    rem = (a1*c2*n2 + a2*c1*n1)//g
    return rem % lcm, lcm



R = 0
M = 1
while True:
    try:
        m, r = [int(t) for t in input().split()]
        R, M = crt((r, m), (R, M))
    except EOFError:
        break

print(Decimal(R).sqrt())