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 (1.42.0) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {
        k:Chars,
        d:usize,
    }
    //剰余を持つ？

    let n = k.len();
    let mut dp = vec![vec![vec![0i64; 2]; d]; n + 1];

    dp[0][0][1] = 1;
    for (i, &c) in k.iter().enumerate() {
        let num = charconv(c, '0');
        for amari in 0..d {
            dp[i + 1][(amari + num) % d][1] += dp[i][amari][1];
            for j in 0..num {
                dp[i + 1][(amari + j) % d][0] += dp[i][amari][1];
            }
            for j in 0..=9 {
                dp[i + 1][(amari + j) % d][0] += dp[i][amari][0];
            }
            dp[i][amari][0] %= MOD;
            dp[i][amari][1] %= MOD;
            dp[i + 1][amari][0] %= MOD;
            dp[i + 1][amari][1] %= MOD;
        }
    }
    // dbg!(&dp);
    println!("{}", (dp[n][0][0] + dp[n][0][1] - 1 + MOD) % MOD);
}
const MOD: i64 = 1000000007;
pub fn charconv(c: char, base: char) -> usize {
    return (c as u8 - base as u8) as usize;
}