{"raw_statement":[{"iden":"problem statement","content":"Snuke bought a bridge of length $L$. He decided to cover this bridge with blue tarps of length $W$ each.\nBelow, a position on the bridge is represented by the distance from the left end of the bridge. When a tarp is placed so that its left end is at the position $x$ ($0 \\leq x \\leq L-W$, $x$ is real), it covers the range $[x, x+W]$. (Note that both ends are included.)\nHe has already placed $N$ tarps. The left end of the $i$\\-th tarp is at the position $a_i$.\nAt least how many more tarps are needed to cover the bridge entirely? Here, the bridge is said to be covered entirely when, for any real number $x$ between $0$ and $L$ (inclusive), there is a tarp that covers the position $x$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 10^{5}$\n*   $1 \\leq W \\leq L \\leq 10^{18}$\n*   $0 \\leq a_1 < a_2 < \\cdots < a_N \\leq L-W$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $L$ $W$\n$a_1$ $\\cdots$ $a_N$"},{"iden":"sample input 1","content":"2 10 3\n3 5"},{"iden":"sample output 1","content":"2\n\n*   The bridge will be covered entirely by, for example, placing two tarps so that their left ends are at the positions $0$ and $7$."},{"iden":"sample input 2","content":"5 10 3\n0 1 4 6 7"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"12 1000000000 5\n18501490 45193578 51176297 126259763 132941437 180230259 401450156 585843095 614520250 622477699 657221699 896711402"},{"iden":"sample output 3","content":"199999992"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}