문제<\/h2>
Lucy is a frequent arcade visitor. All machines at the arcade give out tickets to exchange for prizes! Lucy's favorite machine works as follows.<\/p>
The machine only has two buttons: "Roll" and "Withdraw". Whenever Lucy presses "Roll", the machine increases the counter on the screen by a randomly generated real<\/strong> number between $0<\/mn><\/mrow>0<\/math><\/span><\/span> 0<\/span><\/span><\/span><\/span> and d<\/mi><\/mrow>d<\/math><\/span><\/span> d<\/span><\/span><\/span><\/span>. At any moment, she can press "Withdraw" to get the number of tickets equal to the counter, which gets reset. In case it's not an integer, the machine generously rounds the counter up before handing out the tickets.<\/p> More formally, the machine stores a real number S<\/mi><\/mrow>S<\/math><\/span><\/span> S<\/span><\/span><\/span><\/span>, initially equal to 0. On each "Roll" press, the machine generates Δ<\/mi><\/mrow>\Delta<\/math><\/span><\/span> Δ<\/span><\/span><\/span><\/span> --- a random real<\/strong> number picked uniformly from the interval (<\/mo>0<\/mn>,<\/mo>d<\/mi>)<\/mo><\/mrow>(0, d)<\/math><\/span><\/span> (<\/span> 0<\/span>,<\/span>$

Lucky Number Theory