// 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")); } // Verified by: https://yukicoder.me/submissions/706484 fn ext_gcd(a: i128, b: i128) -> (i128, i128, i128) { if b == 0 { return (a, 1, 0); } let r = a % b; let q = a / b; let (g, x, y) = ext_gcd(b, r); (g, y, x - q * y) } fn inv_mod(a: i128, b: i128) -> i128 { let (_, mut x, _) = ext_gcd(a, b); x %= b; if x < 0 { x += b; } x } // gcd(rm[i].1, rm[j].1) == 1 for i != j // Ref: https://www.creativ.xyz/ect-gcd-crt-garner-927/ // O(n^2) fn garner(rm: &[(i128, i128)], mo: i128) -> i128 { let n = rm.len(); let mut x_mo = (rm[0].0 % rm[0].1) % mo; let mut mp_mo = 1; let mut coef = Vec::with_capacity(n); coef.push(rm[0].0 % rm[0].1); for i in 1..n { let (r, m) = rm[i]; let r = r % m; let mut mp_mi = 1; let mut x_mi = 0; mp_mo = mp_mo * (rm[i - 1].1 % mo) % mo; for j in 0..i { x_mi = (x_mi + mp_mi * (coef[j] % m)) % m; mp_mi = mp_mi * (rm[j].1 % m) % m; } let t = (r - x_mi + m) % m * inv_mod(mp_mi, m) % m; x_mo = (x_mo + t % mo * mp_mo) % mo; coef.push(t); } x_mo } fn zadd(a: i32, b: i32, c: i32) -> i32 { let mut x = a + b; if x >= c { x -= c; } x } fn calc(n: usize, x: &[usize], mo: i32) -> i32 { let n2 = (n + 1) / 2; let mut dp = vec![0i32; n2]; dp[0] = 1; for i in 1..n2 { let mut tmp = 0; for &x in x { if i >= x { tmp = zadd(tmp, dp[i - x], mo); } } dp[i] = tmp; } let mut res = 0i64; for &x in x { for i in 0..n2 { if n - i - 1 >= x && n - i - 1 - x < n - n2 { res += dp[i] as i64 * dp[n - i - 1 - x] as i64; res %= mo as i64; } } } res as i32 } // https://yukicoder.me/problems/no/695 (4, 答えを見た) // この問題の法は 10^{17} + 7 = 17×9920467×592951213 (異なる素因数 3 個) を満たす。 // 素因数ごとに計算することにすれば 1 エントリあたり 4 バイトで済むため、必要なメモリは 20M * 4B = 80MB。 // 両側から DP をして、半分の境界を超えるところを全探索する方式でできる。両側の DP 配列は同じ値になるので、半分のメモリでできる。 fn main() { input! { n: usize, m: usize, x: [usize; m], } let mo = [17, 9920467, 592951213]; let mut res = [(0, 0); 3]; let mut prod = 1i128; for i in 0..3 { res[i] = (calc(n, &x, mo[i]) as i128, mo[i] as i128); prod *= mo[i] as i128; } let res = garner(&res, prod); println!("{}", res); }