Problem D
Help Mr. Tomisu
Input: Standard Input

Output: Standard Output

After wasting a significant time of his life in problem-setting, Mr. Tomisu is now searching for glory: A glory that will make him famous like Goldbach and rich like Bill Gates :). And he has chosen the field of Number Theory as his prime interest. His creator did not make him very bright and so he needs your help to solve an elementary problem, using which he will begin his pursuit for glory!

Tomisu has come to know that finding out numbers having large prime factors are very important in cryptography. Given two integers N and M, he aims to count the number of integers x between 2 and N! (factorial N), having the property that all prime factors of x are greater than M.

Input

The input file contains at most 500 lines of inputs. Each line contains two integers N (1

Output

For each line of input produce one line of output. This line contains the value T % 100000007 (Modulo 100000007 value of T). Here T is the total number of numbers between 1 and N! (factorial N) which have prime factors greater than M. 

Sample Input                                     Output for Sample Input

100 10 100 20 10000 9000 0 0

43274465 70342844 39714141

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Problemsetter: Shahriar Manzoor

Special Thanks: Per Austrin