Faulty Factorial

The factorial of a natural number is the product of all positive integers up to that number. For example, the factorial of $4$ is $1 \times 2 \times 3 \times 4 = 24$. A faulty factorial of length $n$ has the same shape as the factorial of $n$, but exactly one of the multiplied integers is strictly smaller than it should be. The reduced value is still at least $1$. For example, $1 \times 2 \times 2 \times 4 = 16$ is a faulty factorial of length $4$.

You are given the length $n$, a prime modulus $p$, and a target remainder $r$. Find a faulty factorial of length $n$ that leaves remainder $r$ when divided by $p$.

The first line contains the length $n$ of the faulty factorial, the prime modulus $p$, and the target remainder $r$, separated by spaces ($2 \le n \le 10^{18}$, $2 \le p < 10^7$, $0 \le r < p$). The number $p$ is prime.

If no faulty factorial meets the requirement, print -1 -1. Otherwise print the index $k$ of the fault and the value $v$ at that index, separated by a space ($2 \le k \le n$, $1 \le v < k$).

If several pairs work, print the lexicographically smallest pair $(k, v)$. That is, take the smallest $k$, and among the answers with that $k$ take the smallest $v$.

The answer for the first example describes the faulty factorial $1 \times 2 \times 2 \times 4 = 16$. Dividing $16$ by $5$ leaves remainder $1$.