Digit Sum

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

inputFormat

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

outputFormat

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

样例

98765432109876543210
58

635270834