Two Lottery Games

While returning home, you noticed an announcement:

"Select $m$ distinct numbers from the range $1$ to $n$ inclusive. We will randomly select $m$ distinct numbers from the same range. If at least $k$ numbers match, you win."

Calculate the probability of your win.

Input

Each line is a separate test case and contains three integers: $n$, $m$, and $k(2\le n\le 8,1\le m\le n-1,1\le k\le m)$.

Output

For each test case, print the probability of your win, with at least $4$ decimal places.

Examples