{"problem":{"name":"Bridge and Sheets","description":{"content":"Snuke bought a bridge of length $L$. He decided to cover this bridge with blue tarps of length $W$ each. Below, a position on the bridge is represented by the distance from the left end of the bridge.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc134_a"},"statements":[{"statement_type":"Markdown","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 $x$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 10^{5}$\n*   $1 \\leq W \\leq L \\leq 10^{18}$\n*   $0 \\leq a_1 < a_2 < \\cdots < a_N \\leq L-W$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $L$ $W$\n$a_1$ $\\cdots$ $a_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc134_a","tags":[],"sample_group":[["2 10 3\n3 5","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 $7$."],["5 10 3\n0 1 4 6 7","0"],["12 1000000000 5\n18501490 45193578 51176297 126259763 132941437 180230259 401450156 585843095 614520250 622477699 657221699 896711402","199999992"]],"created_at":"2026-03-03 11:01:14"}}