Educational DP Contest AtCoder S - Digit Sum

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Points: 12
Time limit: 0.6s
Memory limit: 1G
Problem types

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 \le K < 10^{10\,000}
  • 1 \le D \le 100

Input Specification

The first line will contain the integer K.

The second line will contain the integer D.

Output Specification

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

Sample Input 1

30
4

Sample Output 1

6

Explanation For Sample 1

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

Sample Input 2

1000000009
1

Sample Output 2

2

Explanation For Sample 2

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

Sample Input 3

98765432109876543210
58

Sample Output 3

635270834

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