You are given integers $A$, $B$, and $M$.

How many permutations $P = (P_1, \dots, P_{AB-1})$ of $(1, 2, \ldots, AB - 1)$ satisfy all of the following conditions? Find the count modulo $M$.

-   The length of a longest increasing subsequence of $P$ is $A$.
-   The length of a longest decreasing subsequence of $P$ is $B$.
-   There exists an integer $n$ such that appending $n + 0.5$ to the end of $P$ does not change either of the lengths of a longest increasing subsequence and a longest decreasing subsequence.

The input is given from Standard Input in the following format:

```
$A$ $B$ $M$
```

Print the number of permutations satisfying the conditions, modulo $M$.

-   All input values are integers.
-   $2 \leq A, B$
-   $AB \leq 120$
-   $10^8 \leq M \leq 10^9$
-   $M$ is a prime.

10

For example, $P = (2, 4, 5, 1, 3)$ satisfies the conditions. This can be confirmed as follows:

-   The length of a longest increasing subsequence of $P$ is $3$.
-   The length of a longest decreasing subsequence of $P$ is $2$.
-   For $n = 4$, the lengths of longest increasing and decreasing subsequences of $(2, 4, 5, 1, 3, 4.5)$ are $3$ and $2$, respectively.

There are $10$ permutations of $(1, 2, 3, 4, 5)$ that satisfy the conditions.