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.

Examples

Input

30
4

Output

6

Input

1000000009
1

Output

2

Input

98765432109876543210
58

Output

635270834

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见题面