Compositeness of Numberland

All the numbers in Numberland wish they had a composed and calm demeanour. In Numberland, this is measured by the compositeness.

The compositeness of a number is the sum of its prime factors, not including itself. Therefore, the compositeness of 12 is 5 = 2 + 3 and the compositeness of a prime number (eg. 19) is 0.

Numberland sometimes sends a team of numbers on a mission. The chances of success depends on the sum of the compositeness of all its members. Your job is to calculate the compositeness of a range of numbers between A and B, so that Numberland may know how likely these numbers are to succeed in their sacred task.

Compositeness knows no 32-bit bounds, 64-bit integers may be required to give a composed answer.

Input

The first line contains two integers A and B ($1 \leq A \leq B \leq 10,000,000$).

Output

Output the total compositeness of all the numbers between A and B inclusive.

Explanation of 1st sample case: The compositeness of each of the numbers between 1 and 10 are 0, 0, 0, 2, 0, 5, 0, 2, 3, 7. Their sum is 19.

Subtasks

• For 20%, $A, B \leq 100$
• For 25%, $A, B \leq 1,200$
• For 25%, $A, B \leq 125,000$
• For the remaining 30%, no additional constraints apply.