We are asked to count the number of sequences of length <code>k + 1</code> that start from <code>(x_s, y_s)</code> and end with <code>(x_d, y_d)</code>. i.e., <code>(x_s, y_s), (x₁, y₁), ..., (x_{k - 1}, y_{k - 1}), (x_d, y_d)</code>.

The key point is to see <code>x</code> and <code>y</code> separately.

Suppose we do <code>i</code> vertical moves and <code>k - i</code> horizontal moves.

In each vertical move, we change only <code>y</code>. Now let's count the number of sequences of length <code>i + 1</code> that start with <code>source[2]</code> and end with <code>dest[2]</code>. Let's call this number <code>vertical_count</code>.

Do the same for horizontal moves and let it be <code>horizontal_count</code>.

For each <code>i</code>, the number of ways would be <code>vertical_count * horizontal_count * C(n, i)</code> since the order of vertical and horizontal moves could be arbitrary.