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 Go (1.14.1) (judge verdict: Accepted)

package main
import "fmt"

/*
i 的遍历顺序从最高位到最低位
T(i, prefix_remainder, isEqual) 表示第 i 位、
更高位的数字和 mod D 为 prefix_remainder、
状态为 isEqual(true 表示前缀与 K 的相应前缀相等，false < K 的相应前缀) 的方案数
则 T(hi, 0, true) 为最终答案，其中 hi = K 的最高位对应的 i，
比如：98765，则最高位 i = 5

状态转移：
T(i, prefix_remainder, isEqual) = 
Sum{ 
	T(i-1, prefix_remainder + d_i, isEqual && d_i == d[i])
	0 <= d_i <= 9 if !isEqual = false or d[i] if isEqual
}
其中，d_i 表示在 i 位上的数字选择，d[i] 表示 K 在 i 位上的数字

边界条件：
T(0, any, any) = 1，遍历到 0 意味着个位数字都已经确定完了

下面的具体实现与上述推导不符
*/

const MAXL = 1e4+5
const MAXD = 105
const MOD = 1e9+7

var n int
var D int
var d [MAXL]int
var T [MAXL][MAXD][2]int

func cast(b bool) int {
  if b {
    return 1
  } else {
    return 0
  }
}

func solve(i int, prefix int, isEqual bool) int {
	if i == n {
      	if prefix == 0 {
        	return 1
      	} else {
        	return 0
      	}
	}
  if T[i][prefix][cast(isEqual)] >= 0 {
		return T[i][prefix][cast(isEqual)]
	}
	maxD := 9
	if isEqual {
		maxD = d[i]
	}
	var sum int64
	for digit := 0; digit <= maxD; digit++ {
      	sum += int64(solve(i+1, (prefix+digit) % D, isEqual && digit == d[i]))
	}
	sum %= MOD
    T[i][prefix][cast(isEqual)] = int(sum)
  	return int(sum)
}

func main() {
	var K string
	fmt.Scanln(&K)
	fmt.Scanln(&D)
	n = len(K)
	for i := 0; i < n; i++ {
      	d[i] = int(K[i] - '0')
	}
	for i := 0; i < n; i++ {
		for j := 0; j < D; j++ {
			T[i][j][0] = -1
          	T[i][j][1] = -1
		}
	}
	
  fmt.Println((MOD + solve(0, 0, true) - 1) % MOD) // minus 1 for 0
}