Problem A
Hash

Little Mirko is studying the hash function which associates numerical values to words. The function is defined recursively in the following way:

• $f(\text{empty word})=0$

• $f(\text{word}+\text{letter})=((f(\text{word})\cdot 33)\oplus \mathrm{ord}(\text{letter}))\mathrm{\%}\mathrm{MOD}$

The function is defined for words that consist of only lowercase letters of the English alphabet. $\oplus$ stands for the bitwise exclusive or operator (i.e. $0110\oplus 1010=1100$), $\mathrm{ord}(\text{letter})$ stands for the ordinal number of the letter in the alphabet ($\mathrm{ord}(\mathtt{a})=1$, $\mathrm{ord}(\mathtt{z})=26$) and $A\mathrm{\%}B$ stands for the remainder of the number $A$ when performing integer division with the number $B$. $\mathrm{MOD}$ will be an integer of the form $2^M$.

Some values of the hash function when $M$ = 10:

• $f(\mathtt{a})=1$

• $f(\mathtt{aa})=32$

• $f(\mathtt{kit})=438$

Mirko wants to find out how many words of the length $N$ there are with the hash value $K$. Write a programme to help him calculate this number.

Input

The first line of input contains three integers $N$, $K$ and $M$ ($1\le N\le 10$, $0\le K<2^M$, $6\le M\le 25$).

Output

The first and only line of output must consist of the required number from the task.

1 0 10

0

1 2 10

1

3 16 10

4