#[doc = " https://github.com/hatoo/competitive-rust-snippets"] #[allow(unused_imports)] use std::cmp::{max, min, Ordering}; #[allow(unused_imports)] use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque}; #[allow(unused_imports)] use std::iter::FromIterator; #[macro_export] macro_rules ! chmax { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: max ( $ x ,$ v ) ; ) + } ; } #[macro_export] macro_rules ! chmin { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: min ( $ x ,$ v ) ; ) + } ; } #[macro_export] macro_rules ! max { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: max ( $ x , max ! ( $ ( $ xs ) ,+ ) ) } ; } #[macro_export] macro_rules ! min { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: min ( $ x , min ! ( $ ( $ xs ) ,+ ) ) } ; } #[macro_export] macro_rules ! dvec { ( $ t : expr ; $ len : expr ) => { vec ! [ $ t ; $ len ] } ; ( $ t : expr ; $ len : expr , $ ( $ rest : expr ) ,* ) => { vec ! [ dvec ! ( $ t ; $ ( $ rest ) ,* ) ; $ len ] } ; } #[doc = " main"] #[allow(unused_imports)] use std::io::{stdin, stdout, BufWriter, Write}; #[macro_export] macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; } #[macro_export] macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; } #[macro_export] macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; } use std::io; use std::io::BufRead; use std::str; pub struct Parser { reader: R, buf: Vec, pos: usize, } impl Parser { pub fn from_str(s: &str) -> Parser { Parser { reader: io::empty(), buf: s.as_bytes().to_vec(), pos: 0, } } } impl Parser { pub fn new(reader: R) -> Parser { Parser { reader: reader, buf: vec![], pos: 0, } } pub fn update_buf(&mut self) { self.buf.clear(); self.pos = 0; loop { let (len, complete) = { let buf2 = self.reader.fill_buf().unwrap(); self.buf.extend_from_slice(buf2); let len = buf2.len(); if len == 0 { break; } (len, buf2[len - 1] <= 0x20) }; self.reader.consume(len); if complete { break; } } } pub fn next(&mut self) -> Result { loop { let mut begin = self.pos; while begin < self.buf.len() && (self.buf[begin] <= 0x20) { begin += 1; } let mut end = begin; while end < self.buf.len() && (self.buf[end] > 0x20) { end += 1; } if begin != self.buf.len() { self.pos = end; return str::from_utf8(&self.buf[begin..end]).unwrap().parse::(); } else { self.update_buf(); } } } } #[allow(unused_macros)] macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } } #[doc = " https://github.com/hatoo/competitive-rust-snippets"] const BIG_STACK_SIZE: bool = true; #[allow(dead_code)] fn main() { use std::thread; if BIG_STACK_SIZE { thread::Builder::new() .stack_size(32 * 1024 * 1024) .name("solve".into()) .spawn(solve) .unwrap() .join() .unwrap(); } else { solve(); } } fn solve() { let out = stdout(); let mut out = BufWriter::new(out.lock()); input!{ n:usize,w:usize,k:i64, a:[usize;n] } let mo = 1_000_000_007; let mut dp: Vec = vec![0.into();500]; dp[0] = 1.into(); for i in 0..2*w { for j in 0..n { let x = dp[i]; dp[i+a[j]] += x; } } let dpw = dp[w]; let dp2w = dp[2*w] - dpw*dpw; let init = Matrix { v: vec![ vec![1], vec![0], ]}; let A = Matrix { v: vec![ vec![dpw.0, dp2w.0], vec![1, 0], ]}; let ans = A.pow(k as u64, 1_000_000_007) * init; writeln!(out,"{}",ans.v[0][0]); } pub mod modular { const M: i64 = 1_000_000_007; #[derive(Debug, Clone, Copy, Default, PartialOrd, Ord, PartialEq, Eq)] pub struct Mod(pub i64); impl ::std::fmt::Display for Mod { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { write!(f, "{}", self.0) } } impl Mod { pub fn new(v: i64) -> Mod { Mod((v + M) % M) } pub fn pow(self, mut r: i64) -> Mod { let mut k = self; let mut ret = 1.into(); while r > 0 { if r % 2 != 0 { ret = ret * k; } r /= 2; k = k * k; } ret } pub fn recip(self) -> Mod { self.pow(M - 2) } } use std::ops::*; impl> Add for Mod { type Output = Mod; fn add(self, rhs: T) -> Self::Output { Mod::new(self.0 + rhs.into().0) } } impl> AddAssign for Mod { fn add_assign(&mut self, rhs: T) { *self = *self + rhs; } } impl> Sub for Mod { type Output = Mod; fn sub(self, rhs: T) -> Self::Output { Mod::new(self.0 - rhs.into().0 + M) } } impl> SubAssign for Mod { fn sub_assign(&mut self, rhs: T) { *self = *self - rhs; } } impl> Mul for Mod { type Output = Mod; fn mul(self, rhs: T) -> Self::Output { Mod::new(self.0 * rhs.into().0) } } impl> MulAssign for Mod { fn mul_assign(&mut self, rhs: T) { *self = *self * rhs; } } impl> Div for Mod { type Output = Mod; fn div(self, rhs: T) -> Self::Output { self * rhs.into().recip() } } impl> DivAssign for Mod { fn div_assign(&mut self, rhs: T) { *self = *self / rhs; } } impl Neg for Mod { type Output = Mod; fn neg(self) -> Self::Output { Mod(0) - self } } impl> ::std::convert::From for Mod { fn from(v: T) -> Self { Mod::new(v.into()) } } } pub type Mod = modular::Mod; pub mod matrix { #[derive(Clone)] pub struct Matrix { pub v: Vec>, } impl Matrix { pub fn identity(n: usize) -> Self { let mut v = vec![vec![0; n]; n]; for i in 0..n { v[i][i] = 1; } Matrix { v: v } } pub fn m(&self) -> usize { self.v.len() } pub fn n(&self) -> usize { self.v[0].len() } pub fn mul_rem(&self, other: &Self, mo: i64) -> Self { assert!(self.n() == other.m()); let K = self.n(); let M = self.m(); let N = other.n(); let mut r = vec![vec![0; N]; M]; for i in 0..M { for j in 0..N { let mut v = 0; for k in 0..K { v += self.v[i][k] * other.v[k][j] % mo; v %= mo; } r[i][j] = v; } } Matrix { v: r } } pub fn pow(&self, k: u64, mo: i64) -> Self { assert!(self.m() == self.n()); let mut k = k; let mut x = Self::identity(self.m()); let mut y = self.clone(); while k > 0 { if k & 1 > 0 { x = y.clone() * x; x %= mo; } y = y.mul_rem(&y, mo); y %= mo; k >>= 1; } x } } use std::ops::*; impl Add for Matrix { type Output = Self; fn add(self, other: Self) -> Self { let mut r = self.v.clone(); for i in 0..self.m() { for j in 0..self.n() { r[i][j] += other.v[i][j]; } } Matrix { v: r } } } impl Sub for Matrix { type Output = Self; fn sub(self, other: Self) -> Self { let mut r = self.v.clone(); for i in 0..self.m() { for j in 0..self.n() { r[i][j] -= other.v[i][j]; } } Matrix { v: r } } } impl Mul for Matrix { type Output = Self; fn mul(self, other: Self) -> Self { assert!(self.n() == other.m()); let K = self.n(); let M = self.m(); let N = other.n(); let mut r = vec![vec![0; N]; M]; for i in 0..M { for j in 0..N { let mut v = 0; for k in 0..K { v += self.v[i][k] * other.v[k][j]; } r[i][j] = v; } } Matrix { v: r } } } impl Rem for Matrix { type Output = Self; fn rem(self, mo: i64) -> Self { let mut r = self.v.clone(); for i in 0..self.m() { for j in 0..self.n() { r[i][j] %= mo; } } Matrix { v: r } } } impl RemAssign for Matrix { fn rem_assign(&mut self, mo: i64) { for i in 0..self.m() { for j in 0..self.n() { self.v[i][j] %= mo; } } } } } pub type Matrix = matrix::Matrix;