pub mod io { use std::io::{BufRead, ErrorKind}; pub fn scan(r: &mut R) -> Vec { let mut res = Vec::new(); loop { let buf = match r.fill_buf() { Ok(buf) => buf, Err(e) if e.kind() == ErrorKind::Interrupted => continue, Err(e) => panic!(e), }; let (done, used, buf) = { match buf.iter().position(u8::is_ascii_whitespace) { Some(i) => (i > 0 || res.len() > 0, i + 1, &buf[..i]), None => (buf.is_empty(), buf.len(), buf), } }; res.extend_from_slice(buf); r.consume(used); if done { return res; } } } #[macro_export] macro_rules! scan { ($r:expr, [$t:tt; $n:expr]) => { (0..$n).map(|_| scan!($r, $t)).collect::>() }; ($r:expr, [$t:tt]) => { scan!($r, [$t; scan!($r, usize)]) }; ($r:expr, ($($t:tt),*)) => { ($(scan!($r, $t)),*) }; ($r:expr, Usize1) => { scan!($r, usize) - 1 }; ($r:expr, Bytes) => { io::scan($r) }; ($r:expr, String) => { String::from_utf8(scan!($r, Bytes)).unwrap() }; ($r:expr, $t:ty) => { scan!($r, String).parse::<$t>().unwrap() }; } #[macro_export] macro_rules! input { ($r:expr, $($($v:ident)* : $t:tt),* $(,)?) => { $(let $($v)* = scan!($r, $t);)* }; } } pub mod mod_int { use std::fmt; use std::ops::*; #[derive(Clone, Copy, Debug)] pub struct ModInt(u64); impl ModInt { const MOD: u64 = 1_000_000_007; pub fn new(mut x: u64) -> Self { if x >= Self::MOD { x %= Self::MOD; } Self(x) } pub fn zero() -> Self { Self(0) } pub fn one() -> Self { Self(1) } } impl From for ModInt { fn from(x: usize) -> Self { Self::new(x as u64) } } impl From for ModInt { fn from(mut x: i64) -> Self { let m = Self::MOD as i64; if x.abs() >= m { x %= m; } if x < 0 { x += m } Self::new(x as u64) } } impl Add for ModInt { type Output = Self; fn add(self, other: Self) -> Self { let mut x = self.0 + other.0; if x >= Self::MOD { x -= Self::MOD; } Self(x) } } impl AddAssign for ModInt { fn add_assign(&mut self, other: Self) { *self = *self + other; } } impl Sub for ModInt { type Output = Self; fn sub(mut self, other: Self) -> Self { if self.0 < other.0 { self.0 += Self::MOD; } Self(self.0 - other.0) } } impl SubAssign for ModInt { fn sub_assign(&mut self, other: Self) { *self = *self - other; } } impl Mul for ModInt { type Output = Self; fn mul(self, other: Self) -> Self { Self::new(self.0 * other.0) } } impl MulAssign for ModInt { fn mul_assign(&mut self, other: Self) { *self = *self * other; } } impl fmt::Display for ModInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "{}", self.0) } } impl ModInt { pub fn pow(mut self, mut n: u64) -> Self { let mut res = Self::one(); while n > 0 { if n & 1 == 1 { res *= self; } self *= self; n >>= 1; } res } pub fn inv(self) -> Self { self.pow(Self::MOD - 2) } } } pub mod combination { use super::mod_int::ModInt; pub struct Combination { fact: Vec, inv_fact: Vec, inv: Vec, } impl Combination { pub fn new(n: usize) -> Combination { let mut fact = vec![ModInt::zero(); n + 1]; let mut inv_fact = vec![ModInt::zero(); n + 1]; let mut inv = vec![ModInt::zero(); n + 1]; fact[0] = ModInt::one(); for i in 1..=n { fact[i] = fact[i - 1] * ModInt::from(i); } inv_fact[n] = fact[n].inv(); for i in (0..n).rev() { inv_fact[i] = inv_fact[i + 1] * ModInt::from(i + 1); } for i in 1..=n { inv[i] = inv_fact[i] * fact[i - 1]; } Combination { fact, inv_fact, inv, } } pub fn fact(&self, i: usize) -> ModInt { self.fact[i] } pub fn inv_fact(&self, i: usize) -> ModInt { self.inv_fact[i] } pub fn inv(&self, i: usize) -> ModInt { self.inv[i] } pub fn p(&self, n: usize, r: usize) -> ModInt { if n < r { ModInt::zero() } else { self.fact[n] * self.inv_fact[n - r] } } pub fn c(&self, n: usize, r: usize) -> ModInt { if n < r { ModInt::zero() } else { self.fact[n] * self.inv_fact[n - r] * self.inv_fact[r] } } } } use mod_int::ModInt; use combination::Combination; fn run(reader: &mut R, writer: &mut W) { input! { reader, n: usize, c: [usize; 9], } let comb = Combination::new(n); let mut sum = ModInt::zero(); let mut p = ModInt::new(1); for _ in 1..=n { for (i, c) in c.iter().enumerate() { sum += ModInt::from(i + 1) * p * ModInt::from(*c) } p *= ModInt::new(10); } let ans = sum * comb.fact(n - 1) * c.iter().fold(ModInt::one(), |acc, c| acc * comb.inv_fact(*c)); writeln!(writer, "{}", ans).ok(); } fn main() { let (stdin, stdout) = (std::io::stdin(), std::io::stdout()); let ref mut reader = std::io::BufReader::new(stdin.lock()); let ref mut writer = std::io::BufWriter::new(stdout.lock()); run(reader, writer); }