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)

use std::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let s: Vec<char> = it.next().unwrap().chars().collect();
    let d: usize = it.next().unwrap().parse().unwrap();
    const MOD: u32 = 1_000_000_007;
    let mut dp = vec![0; d];
    let mut sup = 0;
    for c in s {
        let k = c.to_digit(10).unwrap() as usize;
        let mut next = vec![0; d];
        for i in 0..d {
            for j in 0..10 {
                let x = (i + j) % d;
                next[x] += dp[i];
                next[x] %= MOD;
            }
        }
        for i in 0..k {
            let x = (sup + i) % d;
            next[x] += 1;
            next[x] %= MOD;
        }
        dp = next;
        sup = (sup + k) % d;
    }
    let ans = (dp[0] + MOD - 1 + if sup == 0 {1} else {0}) % MOD;
    println!("{}", ans);
}

fn main() {
    run();
}