use std::cmp::*; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } // Registry. #[derive(Clone, Default, Debug)] struct Reg { a: Vec, inv: std::collections::HashMap, } impl Reg { pub fn new() -> Self { Self::default() } } impl Reg { pub fn get(&mut self, t: &T) -> usize { if !self.inv.contains_key(t) { let idx = self.a.len(); self.a.push(t.clone()); self.inv.insert(t.clone(), idx); } self.inv[t] } // init must have distinct elements. pub fn init(&mut self, init: &[T], f: F) -> Vec> where F: Fn(T) -> Vec { let mut que = std::collections::VecDeque::new(); for t in init { let idx = self.get(t); que.push_back(idx); } let mut n = self.a.len(); let mut vis = vec![false; n]; let mut to = vec![vec![]; n]; while let Some(v) = que.pop_front() { if vis[v] { continue; } let ans = f(self.a[v].clone()); let mut entries = vec![]; for elem in ans { let idx = self.get(&elem); entries.push(idx); if n <= idx { // A newly created entry. n = self.a.len(); vis.resize(n, false); to.resize(n, vec![]); que.push_back(idx); } } vis[v] = true; to[v] = entries; } let mut ans = vec![vec![0; n]; n]; for i in 0..n { for &e in &to[i] { ans[i][e] += 1; } } ans } } fn squmul(a: &[Vec], b: &[Vec], mo: i64) -> Vec> { let n = a.len(); let mut ret = vec![vec![0; n]; n]; for i in 0..n { for j in 0..n { for k in 0..n { ret[i][k] += a[i][j] * b[j][k]; ret[i][k] %= mo; } } } ret } fn squpow(a: &[Vec], mut e: i64, mo: i64) -> Vec> { let n = a.len(); let mut sum = vec![vec![0; n]; n]; for i in 0..n { sum[i][i] = 1; } let mut cur = a.to_vec(); while e > 0 { if e % 2 == 1 { sum = squmul(&sum, &cur, mo); } cur = squmul(&cur, &cur, mo); e /= 2; } sum } const MOD: i64 = 1_000_000_007; // Tags: matrix-exponentiation fn main() { input! { l: i64, n: usize, m: usize, k: [usize; m], } let mut pop = vec![false; n]; for k in k { pop[k - 1] = true; } let mut reg = Reg::new(); let init = (-1, -1); let next = |(x, y)| -> Vec<(i32, i32)> { if (x, y) == (-2, -2) { return vec![(-2, -2); n]; } let mut v = vec![]; for i in 0..n as i32 { if x == i { v.push((x, min(n as i32, y + 1))); } else if x >= 0 && x == y && pop[x as usize] { v.push((-2, -2)); } else { v.push((i, 0)); } } v }; let mat = reg.init(&[init, (-2, -2)], next); let pw = squpow(&mat, l, MOD); let ii = reg.get(&init); let mut tot = pw[ii][reg.get(&(-2, -2))]; for i in 0..n as i32 { if pop[i as usize] { tot += pw[ii][reg.get(&(i, i))]; tot %= MOD; } } println!("{}", tot); }