P6871 [COCI 2013/2014 #6] HASH

Mirko is studying a hash function.

This hash function is defined as follows: - $f(\rm{NULL})=0$ - $f(a_i+s_i)=((f(s_i)\times33)\operatorname{xor}\ \operatorname{ord}(a_i))\bmod MOD$ Here, $a_i$ represents a character and $s_i$ represents a string. Both consist of lowercase letters. - $\operatorname{xor}$ denotes the bitwise XOR operator. - $\operatorname{ord(letter)}$ denotes the position of the letter in the alphabet (for example, $\operatorname{ord(a)=1}$ and $\operatorname{ord(z)= 26}$). $MOD$ is an integer of the form $2^m$. When $m=10$, some values of the hash function are: - $f(\texttt{a})=1$ - $f(\texttt{aa})=32$ - $f(\texttt{kit})=438$ How many words have hash value $k$ and length $n$?

One line containing three integers $n$, $k$, and $m$.

Output one line containing the number of words of length $n$ whose hash value is $k$.

#### Sample Explanation #### Sample 1 Explanation All characters in the alphabet have $\text{ord}$ values that are not $0$. #### Sample 2 Explanation The word is `b`. #### Sample 3 Explanation The words are `dxl`, `hph`, `lxd`, and `xpx`. #### Constraints $1\le n\le 10$，$0\le k