Pirouettes

Given an integer $N$, consider a room of length $2 \times N+2$, represented as the interval $[-N-1, N+1]$. At the center $C=0$ of the room, a ballerina called Costelina Salopeta starts. She performs $T$ dancing steps of length $1$. The first step goes to the right. The room has $2 \times N$ integer coordinates where you can place $K$ obstacles. When the ballerina reaches an obstacle, she trips and performs a pirouette. She then reverses her moving direction, and the obstacle disappears.

You may not place an obstacle at coordinates $-N-1$, $0$, or $N+1$. The walls at $-N-1$ and $N+1$ are permanent obstacles that never disappear. The point $C=0$ is Costelina's starting position.

Given $T$, $N$, and $K$, count the ways to place $K$ obstacles so that Costelina is back at the starting point $C$ after $T$ steps.

The first line contains three integers $T$, $N$ and $K$.

Output a single integer, the answer modulo $10^9+7$.

• $0 \le T \le 200$, $T$ is even
• $1 \le N \le 100$
• $0 \le K \le 2 \times N$