Problems
"Same quantity, sum and product"
"Same quantity, sum and product"
Your task is to write a program, which will count how many different multisets has \textbf{N} elements with sum \textbf{S} and product \textbf{P} (\textbf{1} ≤ \textbf{N} ≤ \textbf{2^\{5 \}= 32}, \textbf{1} ≤ \textbf{S} ≤ \textbf{2^\{15 \}= 32768} and \textbf{1} ≤ \textbf{P} ≤ \textbf{2^\{36 \}= 68719476736}).
Two multisets are considered different when they differ by elements or by quantities of some elements. If two sequences differ by elements’ order only, they are the same multiset.
\InputFile
Input contains three space-separated integers \textbf{N}, \textbf{S} and \textbf{P} in the same line.
\textbf{1} ≤ \textbf{N} ≤ \textbf{2^5=32}, \textbf{1} ≤ \textbf{S} ≤ \textbf{2^15=32768} and \textbf{1} ≤ \textbf{P} ≤ \textbf{2^36=68719476736}.
\OutputFile
Output exactly one integer number --- the quantity of different multisets.
\Note
The \textbf{12} multisets for \textbf{1^st} test case are:
\textbf{1 2 3 4 5 6 7 8 9}
\textbf{1 2 3 4 6 6 6 7 10}
\textbf{1 2 4 4 4 5 7 9 9}
\textbf{1 3 3 3 4 6 7 8 10}
\textbf{1 3 3 4 4 4 7 9 10}
\textbf{1 3 3 4 4 5 6 7 12}
\textbf{2 2 2 3 4 6 7 9 10}
\textbf{2 2 2 3 5 6 6 7 12}
\textbf{2 2 3 3 3 5 7 8 12}
\textbf{2 2 3 3 4 5 6 6 14}
\textbf{2 3 3 3 3 4 5 8 14}
\textbf{2 3 3 3 4 4 4 7 15}
Input example #1
9 45 362880
Output example #1
12