#[allow(unused_imports)] use std::{ cell::RefCell, convert::{Infallible, TryFrom, TryInto as _}, fmt::{self, Debug, Display, Formatter,}, fs::{File}, hash::{Hash, Hasher}, iter::{Product, Sum}, marker::PhantomData, ops::{Add, AddAssign, Sub, SubAssign, Div, DivAssign, Mul, MulAssign, Neg, }, str::FromStr, sync::{atomic::{self, AtomicU32, AtomicU64}, Once}, collections::{*}, mem::{swap}, cmp::{self, Reverse, Ordering, Eq, PartialEq, PartialOrd}, thread::LocalKey, f64::consts::PI, time::Instant, io::{self, stdin, Read, read_to_string, BufWriter, BufReader, stdout, Write}, }; #[allow(unused_imports)] use proconio::{input, input_interactive, marker::{*}}; #[allow(unused_imports)] //use rand::{thread_rng, Rng, seq::SliceRandom}; #[allow(unused_imports)] //use ac_library::{*}; #[allow(dead_code)] const INF: i64 = 1<<60; #[allow(dead_code)] const MOD: i64 = 998244353; #[allow(dead_code)] const D: [(usize, usize); 4] = [(1, 0), (0, 1), (!0, 0), (0, !0)]; pub fn floor(a:i64, b:i64)->i64{let res=(a%b+b)%b;(a-res)/b} pub fn extended_gcd(a:i64,b:i64)->(i64,i64,i64) {if b==0{(a,1,0)}else{let(g,x,y)=extended_gcd(b,a%b);(g,y,x-floor(a,b)*y)}} pub fn mod_inverse(a:i64,m:i64)->i64{let(_,x,_) =extended_gcd(a,m);(x%m+m)%m} pub fn comb(a: i64, b: i64, f: &Vec<(i64, i64)>)->i64{ if aVec<(i64, i64)>{ let mut f=vec![(1i64,1i64),(1, 1)];let mut z = 1i64; let mut inv = vec![0; x as usize+10];inv[1] = 1; for i in 2..x+1{z=(z*i)%MOD; let w=(MOD-inv[(MOD%i)as usize]*(MOD/i)%MOD)%MOD; inv[i as usize] = w; f.push((z, (f[i as usize-1].1*w)%MOD));}return f;} pub fn fast_mod_pow(x: i64,p: usize, m: i64)->i64{ let mut res=1;let mut t=x;let mut z=p;while z > 0{ if z%2==1{res = (res*t)%m;}t = (t*t)%m;z /= 2; }res} #[derive(Clone)] pub struct Matrix{ r: usize, c: usize, v: Vec>, } impl Matrix { pub fn new(r: usize, c: usize, row: &Vec)->Self{ let mut v = Vec::new(); for i in 0..r{ let mut nex = Vec::new(); for j in 0..c{ nex.push(row[i*c+j]); } v.push(nex.clone()); } Matrix{ r, c, v } } pub fn identity(n: usize)->Self{ let mut res = Matrix::new(n, n, &vec![0; n*n]); for i in 0..n{ res.v[i][i] = 1; } res } pub fn zero(n: usize)->Self{ Matrix::new(n, n, &vec![0; n*n]) } pub fn set(&mut self, u: usize, v: usize, x: i64){ self.v[u][v] = x; } pub fn multiply(&mut self, other: &Matrix)->Matrix{ let (n, m) = (self.r, other.c); let mut res = Matrix::new(n, m, &vec![0; n*m]); for i in 0..n{ for j in 0..m{ for k in 0..self.c{ res.v[i][j] = (res.v[i][j]+self.v[i][k]*other.v[k][j])%MOD; } } } res } pub fn pow(&mut self, p: usize)->Matrix{ let mut res = Matrix::identity(self.r); let mut pow = self.clone(); let mut x = p; while x > 0{ if x%2==1{ res = res.multiply(&pow); } x /= 2; let pre = pow.clone(); pow = pow.multiply(&pre); } res } } //use proconio::fastout; //#[fastout] fn main(){ input!{ n: usize, t: usize, k: i64, l: i64, } let mut dp = vec![0; t]; let div = mod_inverse(6, MOD); dp[0] = 1; dp[1] = (k-1)*div%MOD; for i in 2..t{ dp[i] = (dp[i-1]*(k-1)*div%MOD+dp[i-2]*(l-k)*div%MOD)%MOD; } let mut matrix = Matrix::zero(t); for i in 0..t-1{ matrix.set(i, i+1, 1); } matrix.set(t-1, 0, (7-l)*div%MOD); matrix.set(t-1, t-2, (l-k)*div%MOD); matrix.set(t-1, t-1, (k-1)*div%MOD); matrix = matrix.pow(n-1); let mut ans = 0; for i in 0..t{ ans = (ans+matrix.v[0][i]*dp[i])%MOD; } println!("{}", ans); }