Given $N$ and $V$, calculate the result of $\displaystyle\sum_{T \text{ is a labeled unrooted tree with } N \text{ vertices}} f(T)$ modulo $P$.

For a labeled unrooted tree $T$ with $N$ vertices, $f(T)$ is defined as the number of valid ways to assign weights to each vertex. Let $a_i$ be the weight of vertex $i$. An assignment is valid if and only if for all non-empty connected subgraphs $S$ of the tree, the following condition holds:

$$ \text{mex}(\{a_i \mid i \in S\}) = \min(\{a_i \mid i \notin S\}) $$

Here, $\text{mex}(E)$ is defined as the smallest non-negative integer not present in the set $E$, and $\min(E)$ is the minimum element in the set $E$. Specifically, $\text{mex}(\emptyset) = 0$ and $\min(\emptyset) = V + 1$.

Input

A single line containing three integers $N, V, P$.

Output

A single line containing the result of $\displaystyle\sum_{T \text{ is a labeled unrooted tree with } N \text{ vertices}} f(T)$ modulo $P$.

Examples

Input 1

5 3 998244353

Output 1

2280

Input 2, 3, 4

See the provided files.

Constraints

For all test cases, the following holds:

$$ 1 \leq N \leq 150, \quad 1 \leq V \leq 10^9, \quad 3 \leq P \leq 1.01 \times 10^9 $$