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

• $f($empty word$)=0$
• $f($word $+$ letter$)=((f($word$)\times 33)\oplus ord($letter$))\mathrm{\%}MOD$

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

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

• $f($a$)=1$
• $f($aa$)=32$
• $f($kit$)=438$

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

Input Specification

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 Specification

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

Scoring

In test cases worth $30\mathrm{\%}$ of total points, $N$ will not exceed $5$.

Additionally, in test cases worth $60\mathrm{\%}$ of total points, $M$ will not exceed $15$.

Sample Input 1

1 0 10

Sample Output 1

0

Explanation for Sample Output 1

None of the characters in the alphabet has an ord value $0$.

Sample Input 2

1 2 10

Sample Output 2

1

Explanation for Sample Output 2

It is the word b.

Sample Input 3

3 16 10

Sample Output 3

4

Explanation for Sample Output 3

Those are the words dxl, hph, lxd and xpx.