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~)) \mathbin\% 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 \mathbin\% 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\%~ of total points, ~N~ will not exceed ~5~.

Additionally, in test cases worth ~60\%~ 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.