Sequence Growing Hard

Find the number of the possible tuples of sequences (A_0,A_1,...,A_N) that satisfy all of the following conditions, modulo M:

• For every i (0\leq i\leq N), A_i is a sequence of length i consisting of integers between 1 and K (inclusive);
• For every i (1\leq i\leq N), A_{i-1} is a subsequence of A_i, that is, there exists 1\leq x_i\leq i such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};
• For every i (1\leq i\leq N), A_i is lexicographically larger than A_{i-1}.

Constraints

• 1 \leq N,K \leq 300
• 2 \leq M \leq 10^9
• N, K and M are integers.

Input

Input is given from Standard Input in the following format:

N K M

Output

Print the number of the possible tuples of sequences (A_0,A_1,...,A_N), modulo M.

Examples

Input

2 2 100

Output

5

Input

4 3 999999999

Output

358

Input

150 150 998244353

Output

186248260

inputFormat

Input

Input is given from Standard Input in the following format:

N K M

outputFormat

Output

Print the number of the possible tuples of sequences (A_0,A_1,...,A_N), modulo M.

Examples

Input

2 2 100

Output

5

Input

4 3 999999999

Output

358

Input

150 150 998244353

Output

186248260

样例

2 2 100

5