def roll_of_powers_big(a, b):
    if a < 2: return 0, 1
    m = min(i for i in range(b[0]+b[1]) if a**i >= b[0])
    n = 0
    d = b[1] // gcd(b[1], a**m % b[1])
    c = gcd(d, a % b[1])
    while c != 1:
        d = d // c
        c = gcd(d, a % b[1])
        n += 1
    return m + n, euler_phi(d)