A labeled undirected graph is defined as a simple generalized series-parallel graph if and only if:

1. The graph is connected;
2. The graph contains no multiple edges or self-loops;
3. For any $4$ nodes, there do not exist $6$ paths that are pairwise vertex-disjoint (except at endpoints) connecting every pair of these $4$ nodes.

Let $f(i, j)$ denote the number of simple generalized series-parallel graphs with $i$ vertices and $j$ edges.

Given $n, m, p$, you need to calculate $f(i, j) \bmod p$ for all $1 \leq i \leq n$ and $1 \leq j \leq m$.

Input

A single line containing three positive integers $n, m, p$.

Output

Output $n$ lines, each containing $m$ integers, where the $j$-th integer in the $i$-th line represents the value of $f(i, j) \bmod p$.

Examples

Input 1

5 10 998244353

Output 1

0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 
0 3 1 0 0 0 0 0 0 0 
0 0 16 15 6 0 0 0 0 0 
0 0 0 125 222 205 70 0 0 0

Input 2

See additional files.

Constraints

For all test cases, it is guaranteed that:

• $1 \le n, m \le 50$;
• $10^8 \le p \le 10^9+7$, and $p$ is a prime number.

This problem uses bundled testing.

• Subtask 1 (8 points): $n \le 8$, $m \le 10$.
• Subtask 2 (12 points): $n \le 10$, $m \le 20$.
• Subtask 3 (12 points): $n \le 11$, $m \le 20$.
• Subtask 4 (32 points): $n, m \le 25$.
• Subtask 5 (36 points): No additional constraints.