// ---------- begin ModInt ---------- const MOD: u32 = 1_234_567_891; #[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}) } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt((val % MOD as usize) as u32) } } #[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: u32) -> 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 { assert!(self.0 > 0); self.pow(MOD - 2) } } // ---------- end ModInt ---------- use std::io::Read; fn mul(a: &[ModInt], b: &[ModInt], d: &[ModInt]) -> Vec { let len = d.len(); let mut c = vec![ModInt::zero(); 2 * len]; for (i, a) in a.iter().enumerate() { for (c, b) in c[i..].iter_mut().zip(b.iter()) { *c += *a * *b; } } for i in (len..(2 * len)).rev() { let v = c[i]; for j in 1..len { c[i - j] -= v * d[j]; } } c.truncate(len); c } fn run() { let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); let mut it = s.trim().split_whitespace(); let _n: usize = it.next().unwrap().parse().unwrap(); let mut m: u64 = it.next().unwrap().parse().unwrap(); let mut dp = vec![ModInt::one()]; let mut pre = vec![ModInt::zero(); 50 * 500 + 1]; pre[0] = ModInt::one(); for s in it { let a: usize = s.parse().unwrap(); for i in a..pre.len() { pre[i] = pre[i] + pre[i - a]; } let mut next = dp.clone(); for _ in 0..a { next.push(ModInt::zero()); } for (next, dp) in next[a..].iter_mut().zip(dp.iter()) { *next -= *dp; } dp = next; } let len = dp.len(); let mut t = vec![ModInt::zero(); len]; let mut s = vec![ModInt::zero(); len]; t[0] = ModInt::one(); s[1] = ModInt::one(); while m > 0 { if m & 1 == 1 { t = mul(&t, &s, &dp); } s = mul(&s, &s, &dp); m >>= 1; } let mut ans = ModInt::zero(); for i in 0..len { ans += pre[i] * t[i]; } println!("{}", ans); } fn main() { run(); }