#[doc = " https://github.com/akiradeveloper/rust-comp-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 ] } ; } #[macro_export] macro_rules ! cfor { ( ; $ ( $ rest : tt ) * ) => { cfor ! ( ( ) ; $ ( $ rest ) * ) } ; ( $ ( $ init : stmt ) ,+; ; $ ( $ rest : tt ) * ) => { cfor ! ( $ ( $ init ) ,+; ! false ; $ ( $ rest ) * ) } ; ( $ ( $ init : stmt ) ,+; $ cond : expr ; ; $ body : block ) => { cfor ! { $ ( $ init ) ,+; $ cond ; ( ) ; $ body } } ; ( $ ( $ init : stmt ) ,+; $ cond : expr ; $ ( $ step : expr ) ,+; $ body : block ) => { { $ ( $ init ; ) + while $ cond { let mut _first = true ; let mut _continue = false ; loop { if ! _first { _continue = true ; break } _first = false ; $ body } if ! _continue { break } $ ( $ step ; ) + } } } ; } #[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()); let out = stdout(); let mut out = BufWriter::new(out.lock()); input!{ n:usize, c:[usize;9], } let comb = ModComb::new(300000, 1_000_000_007); // b[i]があるところに現れる回数 let mut b: Vec = vec![0.into();9]; for i in 0..9 { b[i] = if c[i] > 0 { let mut k = comb.fact(n-1).into(); for j in 0..9 { if j == i { k *= comb.fact_inv[c[j]-1]; } else { // dbg!(c[j]); k *= comb.fact_inv[c[j]]; } } k } else { 0.into() }; } // dbg!(&b) let mut sum: Mod = 0.into(); let mut x: Mod = 1.into(); for i in 0..n { sum += x; x *= 10; } // dbg!(sum); let mut ans: Mod = 0.into(); for i in 0..9 { ans += Mod::from(i as i64 +1) * sum * b[i]; } println!("{}",ans); } #[derive(Clone)] struct ModComb { fact: Vec, fact_inv: Vec, n: usize, p: i64, } impl ModComb { fn initialize(ft: &mut Self) { let n = ft.n; ft.fact[0] = 1; for i in 1..n { ft.fact[i] = (ft.fact[i - 1] * i as i64) % ft.p; } ft.fact_inv[n - 1] = modpow(ft.fact[n - 1], ft.p - 2, ft.p); for i in (0..n - 1).rev() { ft.fact_inv[i] = (ft.fact_inv[i + 1] * (i + 1) as i64) % ft.p; } } #[doc = "O(N)"] fn new(max_n: usize, p: i64) -> ModComb { let mut ft = ModComb { fact: vec![0; max_n + 1], fact_inv: vec![0; max_n + 1], n: max_n + 1, p: p, }; Self::initialize(&mut ft); ft } fn fact(&self, n: usize) -> i64 { self.fact[n] } #[doc = "choose k numbers from 1..n"] fn nCk(&self, n: i64, k: i64) -> i64 { if n < k { return 0; } (self.nPk(n, k) * self.fact_inv[k as usize]) % self.p } fn nPk(&self, n: i64, k: i64) -> i64 { if n < k { return 0; } self.fact[n as usize] * self.fact_inv[(n - k) as usize] % self.p } #[doc = "split k into n number as x1+x2+...xn=k"] fn nHk(&self, n: i64, k: i64) -> i64 { if n == 0 && k == 0 { return 1; } self.nCk(n + k - 1, k) } #[doc = "put n balls into k different boxes. In case of n=3,k+2 [[1,2],[3]]==[[3],[1,2]]"] fn nSk(&self, n: i64, k: i64) -> i64 { if n < k { return 0; } let mut res = 0; for i in 0..k + 1 { let v = self.nCk(k, i) * modpow(i, n, self.p) % self.p; if (k - i) % 2 == 1 { res = (res + self.p - v) % self.p; } else { res = (res + v) % self.p; } } return res * self.fact_inv[k as usize] % self.p; } fn nBk(&self, n: i64, k: i64) -> i64 { 0 } } #[allow(dead_code)] #[doc = " x ^ n % m"] pub fn modpow(x: i64, n: i64, m: i64) -> i64 { let mut res = 1; let mut x = x % m; let mut n = n; while n > 0 { if n & 1 == 1 { res = (res * x) % m; } x = (x * x) % m; n >>= 1; } res } #[doc = " モジュラ逆元"] #[doc = " "] #[doc = " ax = 1"] #[doc = " を満たすxをaの逆元という。"] #[doc = " "] #[doc = " aとpが素の場合、"] #[doc = " フェルマーの小定理より"] #[doc = " a^(p-1) = 1 (mod p)"] #[doc = " だから、"] #[doc = " a a^(p-2) = 1 (mod p)"] #[doc = " がいえる。"] #[doc = " これよりa^(p-2)はaの逆元であることがいえる。"] 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;