{"raw_statement":[{"iden":"problem statement","content":"You will play a game against a dealer. The game uses a $D$\\-sided die (dice) that shows an integer from $1$ to $D$ with equal probability, and two variables $x$ and $y$ initialized to $0$. The game proceeds as follows:\n\n*   You may perform the following operation any number of times: roll the die and add the result to $x$. You can choose whether to continue rolling or not after each roll.\n    \n*   Then, the dealer will repeat the following operation as long as $y < L$: roll the die and add the result to $y$.\n    \n*   If $x > N$, you lose. Otherwise, you win if $y > N$ or $x > y$ and lose if neither is satisfied.\n    \n\nDetermine the probability of your winning when you act in a way that maximizes the probability of winning."},{"iden":"constraints","content":"*   All inputs are integers.\n*   $1 \\leq L \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq D \\leq N$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $L$ $D$"},{"iden":"sample input 1","content":"3 2 2"},{"iden":"sample output 1","content":"0.468750000000000\n\nIt can be proved that the optimal strategy is to continue rolling as long as $x$ is not greater than $2$."},{"iden":"sample input 2","content":"200000 200000 200000"},{"iden":"sample output 2","content":"0.999986408692793"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}