Euler 160: Find Non-Trivial 5 Digits Factorial

Question

Given the number, find 5 digits before completing 0. 9! = 362880 so f (9) = 36288 10! = 3628800, so f (10) = 36288 20! = 2432902008176640000 so f (20) = 17664 Find f ( 1,000,000,000,000)

To do this, I calculated f(10^6), and then f(10^12) = (f(10^6))^(10^6)to calculate f(n)... I calculate the factorial by removing any 5 and corresponding 2 so that all trailing zeros are removed.
But I get the wrong answer.
Is there a problem in the approach or some kind of stupid mistake?

Code for reference

long long po(long long n, long long m, long long mod) {
    if (m == 0) return 1;
    if (m == 1) return n % mod;
    long long r = po(n, m / 2, mod) % mod;
    if (m % 2 == 0) return (r * r) % mod;
    return (((r * r) % mod) * n) % mod;
}

void foo() {
    unsigned long long i, res = 1, m = 1000000 , c = 0, j, res1 = 1, mod;
    mod = ceil(pow(10, 9));
    cout << mod << endl;
    long long a = 0, a2 = 0, a5 = 0;
    for (i = 1 ; i <= m; i++) {
        j = i;
        while (j % 10 == 0)
            j /= 10;
        while (j % 2 == 0) {
            j /= 2;
            a2++;
        }
        while (j % 5 == 0) {
            j /= 5;
            a5++;
        }
        res = (res * j ) % mod;
    }

    a = a2 - a5;

    for (i = 1; i <= a; i++)
        res = (res * 2) % mod;
    for (i = 1; i <= 1000000; i++) {
        res1 = (res1 * res) % mod;
    }
    cout << res1 << endl;
}

Answer 1

Your equality f(10^12) = (f(10^6))^(10^6)is wrong. f () is based on factorials, not powers.

Answer 2

:

• f (10 ^ 12) f (10 ^ 6) ^ (10 ^ 6).
• 0 , 10, 2 5 . 10 , 5 2 2 5 , 5 2 .

10, 10 ^ 9 , 10 ^ 9 * 10 ^ 12 64- unsigned long long.