Hello codeforces!

I am wondering is there a way to caculate prefix sums $$$k$$$ times modulo $$$p$$$ fast, especially when we can't use matrix multiplication?

By calculating prefix sums $$$k$$$ times I mean this piece of code:

for(int it = 0; it < k; it++) {
    for(int i = 1; i < n; i++)
        pref[i]+= pref[i-1];
}

So if we start with array: $$$1, 0, 0, 0$$$ we will get:

1. $$$1, 1, 1, 1$$$;

2. $$$1, 2, 3, 4$$$;

3. $$$1, 3, 6, 10$$$;

4. $$$1, 4, 10, 20$$$; ...