One method uses formula a4=(t1^4-6*t1^2*t2+3*t2^2+8*t1*t3-6*t4)/24 mod p
For it we must find previously 24^(-1) mod p
But it needs in loop with ~ p=10^9 iterations
May this calculation lead to TL before main program?

Why can't we use extended euclid?

or use fermat little theorem

a^(p-1) = 1 (mod p)
a^(p-2).a = 1 (mod p)

so a^(-1) = a^(p-2) :)

// O(a)
inline int inv(int a)
{
    for (int i = 1; ; i++)
    {
        int64 b = (int64) P * i + 1;
        if (b % a == 0)
            return int(b / a);
    }
    return 0;
}

Best advise was extended evclid
I could apply it during the context.
But 1560 wuild bettter to solve in Java using BigInt
We simply use /24 at the end and avoid many %p operations.

a/b mod p = a*b^-1 mod p = a*b^(-1 mod p-1) mod p = a*b^(p-2) mod p. b^(p-2) can be precomputed using logarithmic powering. I needed only divisors 2, 6 and 24.