Stirling Number

The Stirling number of the first kind $\begin{bmatrix} n \\ k \end{bmatrix}$ is the number of permutations of $n$ elements with exactly $k$ disjoint cycles. The well-known recurrence is

$\begin{bmatrix} n+1 \\ k \end{bmatrix} = n \begin{bmatrix} n \\ k \end{bmatrix} + \begin{bmatrix} n \\ k-1 \end{bmatrix}$

for $k>0$, with the initial conditions

$\begin{bmatrix} 0 \\ 0 \end{bmatrix} = 1 \quad \text{and} \quad \begin{bmatrix} n \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ n \end{bmatrix} = 0$

for $n>0$.

Given four integers $n$, $l$, $r$, and $p$, find the value of

$\left(\sum_{k=l}^{r}{\begin{bmatrix} n \\ k \end{bmatrix}} \right) \bmod p$

where $p$ is prime.

The first line contains four integers $n$, $l$, $r$, and $p$ ($1 \le n \le 10^{18}$, $0 \le l \le r \le n$, $2 \le p \le 10^6$, $p$ is prime).

Output an integer denoting the answer.