Problem:
Score : 1200 points

Problem Statement

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.

Sample Input 1

2 2 100

Sample Output 1

5

Five tuples below satisfy the conditions:

(),(1),(1,1)

(),(1),(1,2)

(),(1),(2,1)

(),(2),(2,1)

(),(2),(2,2)

Sample Input 2

4 3 999999999

Sample Output 2

358

Sample Input 3

150 150 998244353

Sample Output 3

186248260

Solution in Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

var
 a,b,c,i,j,k:longint;
 f:array[0..500,0..500,0..500]of longint;
begin 
 readln(a,b,c);
 f[0,1,0]:=1;
 for i:=1 to a do
  for j:=1 to b do
   for k:=i downto 0 do
    if f[i,j,k]<>0 then
     begin
      if k<>0 then
       begin
        f[i,j,k]:=f[i,j,k] mod c;
        f[i,j,k-1]:=f[i,j,k-1]+f[i,j,k];
       end
      else
       f[i,j+1,i]:=(f[i,j+1,i]+f[i,j,k])mod c;
      f[i+1,j,k]:=(f[i+1,j,k]+(k+1)*f[i,j,k])mod c;
     end;
 writeln(f[a,b+1,a]);
end.