#![allow(unused_imports)] fn main() { input! { n: u64, m: usize, k: usize, } let mut cnt = vec![0; m + 1]; for i in 1..=m { cnt[m / i] += 1; } let mut nonzero = vec![]; for (i, c) in cnt.into_iter().enumerate() { if c != 0 { nonzero.push((i, c)); } } let l = nonzero.len(); let mut mat = mvec![0; (l, l)]; for (i, &(d, c)) in nonzero.iter().enumerate() { for (j, &(dd, _)) in nonzero.iter().enumerate() { if d.abs_diff(dd) <= k { mat[i][j] += c; } } } mat = mat_pow(mat, n - 1); let mut ans = 0; for i in 0..l { for j in 0..l { ans += mat[i][j] * nonzero[j].1; ans %= MOD; } } println!("{ans}"); } fn mat_prod(a: &[Vec], b: &[Vec]) -> Vec> { let n = a.len(); let mut c = mvec![0; (n, n)]; for i in 0..n { for k in 0..n { for j in 0..n { c[i][j] += a[i][k] * b[k][j]; c[i][j] %= MOD; } } } c } fn mat_pow(mut a: Vec>, mut p: u64) -> Vec> { let n = a.len(); let mut r = mvec![0; (n, n)]; for i in 0..n { r[i][i] += 1; } while p > 0 { if p & 1 == 1 { r = mat_prod(&r, &a); } a = mat_prod(&a, &a); p >>= 1; } r } const MOD: u64 = 998244353; /* dp[i+1][a] = cnt[a] * (dp[i][a-38] + .. + dp[i][a+38]) non zero value => O(sqrt m) 2 3 1 [0, 2, 0, 1] [0, 4, 0, 1] */ use proconio::{input, marker::*}; use std::{cmp::Reverse, collections::*}; #[macro_export] macro_rules! chmax { ($a:expr, $b:expr) => {{ let tmp = $b; if $a < tmp { $a = tmp; true } else { false } }}; } #[macro_export] macro_rules! chmin { ($a:expr, $b:expr) => {{ let tmp = $b; if $a > tmp { $a = tmp; true } else { false } }}; } #[macro_export] /// mvec![] macro_rules! mvec { ($val:expr; ()) => { $val }; ($val:expr; ($size:expr $(,$rest:expr)*)) => { vec![mvec![$val; ($($rest),*)]; $size] }; }