#![allow(unused_imports)] #![allow(non_snake_case, unused)] use std::cmp::*; use std::collections::*; use std::ops::*; macro_rules! eprint { ($($t:tt)*) => {{ use ::std::io::Write; let _ = write!(::std::io::stderr(), $($t)*); }}; } macro_rules! eprintln { () => { eprintln!(""); }; ($($t:tt)*) => {{ use ::std::io::Write; let _ = writeln!(::std::io::stderr(), $($t)*); }}; } macro_rules! dbg { ($v:expr) => {{ let val = $v; eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val); val }} } macro_rules! mat { ($($e:expr),*) => { Vec::from(vec![$($e),*]) }; ($($e:expr,)*) => { Vec::from(vec![$($e),*]) }; ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) }; ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) }; } macro_rules! ok { ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => { $a$([$i])*.$f($($t),*) }; ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { { let t = $e; ok!($a$([$i])*.$f($($es),*)$(@$t)*@t) } }; } pub fn readln() -> String { let mut line = String::new(); ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e)); line } macro_rules! read { ($($t:tt),*; $n:expr) => {{ let stdin = ::std::io::stdin(); let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| { let line = line.unwrap(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }).collect::>(); ret }}; ($($t:tt),*) => {{ let line = readln(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }}; } macro_rules! _read { ($it:ident; [char]) => { _read!($it; String).chars().collect::>() }; ($it:ident; [u8]) => { Vec::from(_read!($it; String).into_bytes()) }; ($it:ident; usize1) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::().unwrap_or_else(|e| panic!("{}", e)) - 1 }; ($it:ident; [usize1]) => { $it.map(|s| s.parse::().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::>() }; ($it:ident; [$t:ty]) => { $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::>() }; ($it:ident; $t:ty) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e)) }; ($it:ident; $($t:tt),+) => { ($(_read!($it; $t)),*) }; } pub fn main() { let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join(); } const MOD: u32 = 1_000_000_007; const INF: i64 = std::i64::MAX/2; pub trait SetMinMax { fn setmin(&mut self, v: Self) -> bool; fn setmax(&mut self, v: Self) -> bool; } impl SetMinMax for T where T: PartialOrd { fn setmin(&mut self, v: T) -> bool { *self > v && { *self = v; true } } fn setmax(&mut self, v: T) -> bool { *self < v && { *self = v; true } } } #[derive(Clone, Copy)] struct ModInt(u32); impl std::ops::Add for ModInt { type Output = ModInt; fn add(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::AddAssign for ModInt { fn add_assign(&mut self, rhs: ModInt) { *self = *self + rhs; } } impl std::ops::Sub for ModInt { type Output = ModInt; fn sub(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + MOD - rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::SubAssign for ModInt { fn sub_assign(&mut self, rhs: ModInt) { *self = *self - rhs; } } impl std::ops::Mul for ModInt { type Output = ModInt; fn mul(self, rhs: ModInt) -> Self::Output { ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32) } } impl std::ops::MulAssign for ModInt { fn mul_assign(&mut self, rhs: ModInt) { *self = *self * rhs; } } impl std::ops::Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { ModInt(if self.0 == 0 {0} else {MOD - self.0}) } } #[allow(dead_code)] impl ModInt { pub fn new(n: u32) -> ModInt { ModInt(n % MOD) } pub fn zero() -> ModInt { ModInt(0) } pub fn one() -> ModInt { ModInt(1) } pub fn pow(self, mut n: i64) -> ModInt { let mut t = ModInt::one(); let mut s = self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(self) -> ModInt { self.pow((MOD - 2) as i64) } } fn mul(A: &Vec>, B: &Vec>, _MOD: i64) -> Vec> { let mut C: Vec> = Vec::new(); for i in 0usize..A.len() { let mut c: Vec = (0usize..B[0].len()).map(|v| 0i64).collect(); //iter::repeat(0i64).take(B[0].len()).collect()?? // vec![0i64;B[0].len()]; ?? C.push(c); } for i in 0usize..A.len() { for k in 0usize..B.len() { if A[i][k] == 0 { continue; } for j in 0usize..B[0].len() { C[i][j] += A[i][k] * B[k][j]; C[i][j] %= _MOD; } } } C } fn pow(A: &Vec>, n: i64, _MOD: i64) -> Vec> { let mut A = A.clone(); let mut n = n.clone(); let mut B: Vec> = Vec::new(); for i in 0usize..A.len() { let mut b: Vec = (0usize..A.len()).map(|v| 0i64).collect(); B.push(b); } for i in 0usize..A.len() { B[i][i] = 1; } while n > 0 { if n % 2 == 1 { B = mul(&B, &A, _MOD); } A = mul(&A, &A, _MOD); n >>= 1; } B } fn solve() { let (n,w,k) = read!(usize,usize,i64); let a = read!([usize]); let mut dp = vec![ModInt(0); 1000]; dp[0] = ModInt(1); for i in 0..100 { for j in 0..n { let tmp = dp[i]; dp[i+a[j]] += tmp; } } // for i in 0..11 { // println!("{}", dp[i].0); // } let s = dp[w*2] - dp[w]*dp[w]; let mut F:Vec> = vec![vec![0;2];2]; F[0][0] = dp[w].0 as i64; F[0][1] = s.0 as i64; F[1][0] = 1; let rF = pow(&F,k-1,MOD as i64); let mut ans = ModInt((rF[0][0]%(MOD as i64)) as u32)*(dp[w]); ans += ModInt((rF[0][1]%(MOD as i64)) as u32); if k==1 { println!("{}", dp[w].0); return; } println!("{}", ans.0); } fn run() { solve(); }