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(non_snake_case)]

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());

    let K = scan.chars();
    let D = scan.read::<usize>();
    let n = K.len();
    let mut dp = vec3(n+1, 2, D, Co(0));
    dp[0][0][0] = Co(1);

    for i in 0..n {
        for less in 0..2 {
            let c = K[i] as usize - '0' as usize;
            for d in 0..(if less==1 {10} else {c+1}) {
                for e in 0..D {
                    dp[i+1][less | (d < c) as usize][(d + e) % D] += dp[i][less][e];
                }
            }
        }
    }
    println!("{}", dp[n][0][0] + dp[n][1][0] - Co(1));
}

#[allow(dead_code)]
fn vec2<T: Clone>(a: usize, b: usize, init: T) -> Vec<Vec<T>> {
    vec![vec![init;b];a]
}

#[allow(dead_code)]
fn vec3<T: Clone>(a: usize, b: usize, c: usize, init: T) -> Vec<Vec<Vec<T>>> {
    vec![vec![vec![init;c];b];a]
}

#[allow(dead_code)]
const M: i64 = 1_000_000_007;

#[allow(dead_code)]
use std::ops::*;


#[allow(dead_code)]
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct Co (pub i64);


#[allow(dead_code)]
impl Co {
    pub fn pow(self, mut n: i64) -> Self {
        let mut a = self;
        let mut res = Co(1);
        while n > 0 {
            if n & 1 == 1 {
                res *= a;
            }
            a = a * a;
            n >>= 1;
        }
        res
    }
}


#[allow(dead_code)]
impl std::fmt::Display for Co {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}


macro_rules! impl_from {
    ($($tpe:ident),*) => {
        $(impl From<$tpe> for Co {
            fn from(value: $tpe) -> Self {
                Co((value as i64 % M + M) % M)
            }
        })*
    }
}


impl_from! (i64, u64, usize);


macro_rules! impl_binop {
    ($op:ident,$atr:ident,$assign:ident $(,$optr:ident)*) => {
        impl $atr for Co {
            fn $assign(&mut self, other: Self) {
                *self = self.$op(other);
            }
        }
        $(impl $optr for Co {
            type Output = Self;
            fn $op(self, other: Self) -> Self {
                Co::from((self.0).$op(other.0))
            }
        })*
    }
}


impl_binop! (add, AddAssign, add_assign, Add);

impl_binop! (sub, SubAssign, sub_assign, Sub);

impl_binop! (mul, MulAssign, mul_assign, Mul);

impl_binop! (div, DivAssign, div_assign);


#[allow(dead_code)]
impl Div for Co {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        self * rhs.pow((M - 2) as i64)
    }
}

// region template
#[allow(dead_code)]
fn iu(i: isize) -> usize { i as usize }

#[allow(dead_code)]
fn ui(i: usize) -> isize { i as isize }

#[allow(dead_code, deprecated)]
fn join<T: std::fmt::Display>(slice: &[T], sep: &str) -> String {
    let strings = slice.iter().map(|t| format!("{}", t)).collect::<Vec<_>>();
    strings.connect(sep)
}

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        let mut ret = vec![];
        for _ in 0..n { ret.push(self.read::<T>()) }
        ret
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion