Sequences

Count the number of all non-decreasing sequences of length $n$ containing integers from $1$ to $m$, where every element can occur at most $k$ times.

Input

Three integers $n,m$ and $k(0<n,m,k<31)$.

Output

Print the number of described sequences.

Examples

The sequences are: $(1,1,2),(1,1,3),(1,1,4),(1,2,2),(1,2,3),(1,2,4),(1,3,3),(1,3,4),(1,4,4),(2,2,3),(2,2,4),(2,3,3),(2,3,4),(2,4,4),(3,3,4),(3,4,4)$.