Problem:
Score : 100 points

Problem Statement

Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:

The sum of the digits in base ten is a multiple of D.

Constraints

All values in input are integers.

1 \leq K < 10^{10000}

1 \leq D \leq 100

Input

Input is given from Standard Input in the following format:

K
D

Output

Print the number of integers satisfying the condition, modulo 10^9 + 7.

Sample Input 1

30
4

Sample Output 1

6

Those six integers are: 4, 8, 13, 17, 22 and 26.

Sample Input 2

1000000009
1

Sample Output 2

2

Be sure to print the number modulo 10^9 + 7.

Sample Input 3

98765432109876543210
58

Sample Output 3

635270834

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; let mut next = || { iter . next ( ) . unwrap ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let mut bytes = std :: io :: Read :: bytes ( std :: io :: BufReader :: new ( stdin . lock ( ) ) ) ; let mut next = move || -> String { bytes . by_ref ( ) . map ( | r | r . unwrap ( ) as char ) . skip_while ( | c | c . is_whitespace ( ) ) . take_while ( | c |! c . is_whitespace ( ) ) . collect ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! input_inner { ( $ next : expr ) => { } ; ( $ next : expr , ) => { } ; ( $ next : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! read_value { ( $ next : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ next , $ t ) ) ,* ) } ; ( $ next : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ next : expr , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 } ; ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) } ; }

#[allow(unused_macros)]
macro_rules ! vec_md { ( $ init : expr ; $ ( $ dim : expr ) ;* ) => { vec_md ! ( $ ( $ dim ) ;* => $ init ) } ; ( $ head : expr ; $ ( $ tail : expr ) ;* => $ init : expr ) => { vec ! [ vec_md ! ( $ ( $ tail ) ;* => $ init ) ; $ head ] } ; ( $ head : expr => $ init : expr ) => { vec ! [ $ init ; $ head ] } ; }

#[allow(dead_code)]
pub const M: u64 = 1_000_000_007;

fn main() {
    input! {
        k: chars,
        d: usize
    }
    let k_digits = k.into_iter().map(|c| (c as u8 - b'0') as usize).collect::<Vec<_>>();
    let n = k_digits.len();
    let mut dp = vec_md![Co(0);n+1;d;2];
    dp[0][0][0] = Co(1);
    for i in 0..n {
        for j in 0..d {
            for less in 0..2 {
                for z in 0..(if less == 0 {k_digits[i]+1} else {10}) {
                    let tmp = dp[i][j][less];
                    dp[i+1][(j + z) % d][less | (z < k_digits[i]) as usize]
                        += tmp;
                }
            }
        }
    }
    let ret = dp[n][0][0] + dp[n][0][1];
    println!("{}", ret - Co(1));
}

#[allow(dead_code)]
use std::ops::*;
#[allow(dead_code)]
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
struct Co(u64);
#[allow(dead_code)]
impl std::fmt::Display for Co {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
#[allow(dead_code)]
impl Add for Co {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        Co((self.0 + rhs.0) % M)
    }
}
#[allow(dead_code)]
impl AddAssign for Co {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}
#[allow(dead_code)]
impl Div for Co {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        Co(self.0 * modinv(rhs.0) % M)
    }
}
#[allow(dead_code)]
impl DivAssign for Co {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}
#[allow(dead_code)]
impl Mul for Co {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        Co(self.0 * rhs.0 % M)
    }
}
#[allow(dead_code)]
impl MulAssign for Co {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}
#[allow(dead_code)]
impl Sub for Co {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        Co(sub_mod(self.0, rhs.0))
    }
}
#[allow(dead_code)]
impl SubAssign for Co {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}
#[allow(dead_code)]
fn sub_mod(a: u64, b: u64) -> u64 {
    let mut tmp = (a as i64 - b as i64) % M as i64;
    if tmp < 0 {
        tmp += M as i64;
    }
    tmp as u64
}
#[allow(dead_code)]
fn modinv(a_: u64) -> u64 {
    let m = M as i64;
    let mut a = a_ as i64;
    let mut b = m as i64;
    let mut u = 1;
    let mut v = 0;
    while b != 0 {
        let t = a / b;
        a -= t * b;
        std::mem::swap(&mut a, &mut b);
        u -= t * v;
        std::mem::swap(&mut u, &mut v);
    }
    u %= m;
    if u < 0 {
        u += m
    };
    u as u64
}