{"problem":{"name":"Enormous Atcoder Railroad","description":{"content":"There is a railroad company in Atcoder Kingdom, \"Atcoder Railroad\".   There are $N + 1$ stations numbered $0, 1, 2, ..., N$ along a railway.   Currently, two kinds of train are operated, local and exp","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"s8pc_4_e"},"statements":[{"statement_type":"Markdown","content":"There is a railroad company in Atcoder Kingdom, \"Atcoder Railroad\".  \nThere are $N + 1$ stations numbered $0, 1, 2, ..., N$ along a railway.  \nCurrently, two kinds of train are operated, local and express.  \nA local train stops at every station, and it takes one minute from station $i$ to $i + 1$, and vice versa.  \nAn express train only stops at station $S_0, S_1, S_2, ..., S_{K-1} (0 = S_0 < S_1 < S_2 < ... < S_{K-1} = N)$. It takes one minute from station $S_i$ to $S_{i + 1}$, and vice versa.  \nBut the president of Atcoder Railroad, Semiexp said it is not very convenient so he planned to operate one more kind of train, \"semi-express\".  \nThe stations where the semi-express stops (This is $T_0, T_1, T_2, ..., T_{L-1}$, $0 = T_0 < T_1 < T_2 < ... < T_{L-1} = N$) have to follow following conditions:  \nFrom station $T_i$ to $T_{i+1}$ takes 1 minutes, and vice versa.  \n\n*   The center of Atcoder Kingdom is station $0$, and you have to be able to go to station $i$ atmost $X$ minutes.\n*   If the express stops at the station, semi-express should stops at the station.\n\nPrint the number of ways of the set of the station where semi-express stops (sequence $T$).  \nSince the answer can be large, print the number modulo $10^9 + 7$.\n\n## Input Format\n\n$N$ $K$ $X$\n$S_0$ $S_1$ $S_2$ ... $S_{K-1}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"s8pc_4_e","tags":[],"sample_group":[],"created_at":"2026-03-03 11:01:14"}}