C# Ladder
static int[] Ladder(int[] a, int[] b)
{
    var size = a.Length;
    var r = new int[size];
    var mod = (1 << b.Max()) - 1;

    var limit = a.Max();
    var fib = new int[limit + 2];
    fib[0] = 0;
    fib[1] = 1;
    for (int i = 2; i < limit + 2; i++)
    {
        fib[i] = (fib[i - 1] + fib[i - 2]) & mod;
    }

    for (int i = 0; i < size; i++)
    {
        r[i] = fib[a[i] + 1] & ((1 << b[i]) - 1);
    }

    return r;
}

This precomputes climb counts once and applies the modulo per query, which avoids recalculating the same paths over and over.