Problem Description

Given two positive integers $ A $ and $ B $. Find the number of positive integers that are divisors of $ A! $ and multiples of $ B! $, modulo $ 1,000,000,007 $.

Input Format

The input is given from the standard input in the following format:

$ A $ $ B $

• The first line contains two integers $ A $ and $ B $ ($1 \leq B \leq A \leq 10^9$, $A - B \leq 100$) separated by a space.

Output Format

Output the number of positive integers that satisfy the condition, modulo $ 1,000,000,007 $, on the first line.

Do not forget the newline at the end.

Sample Input and Output

Sample Input #1

3 2

Sample Output #1

2

Sample Input #2

15 4

Sample Output #2

2592

Sample Input #3

1000000 999900

Sample Output #3

21398499

Sample Input #4

1000000000 999999900

Sample Output #4

745508745

Notes/Hints

Partial Points

This problem has partial points.

• $ 5 $ points for test cases where $1 \leq B \leq A \leq 15$.
• Another $ 35 $ points for test cases where $1 \leq B \leq A \leq 10^6$, $A - B \leq 100$.

Sample Explanation 1

For a positive integer $ n $, $ n! $ represents the factorial of $ n $, which is $n \times (n - 1) \times (n - 2) \times \ldots \times 1$. The divisors of $3! = 3 \times 2 \times 1 = 6$ that are also multiples of $2! = 2 \times 1 = 2$ are $ 2 $ and $ 6 $, totaling $ 2 $ numbers.

见题面 Input 部分

见题面 Output 部分