D. Soldier and Number Game
time limit per test3 seconds
memory limit per test256 megabytes
Two soldiers are playing a game. At the beginning first of them chooses a positive integer n and gives it to the second soldier. Then the second one tries to make maximum possible number of rounds. Each round consists of choosing a positive integer x > 1, such that n is divisible by x and replacing n with n / x. When n becomes equal to 1 and there is no more possible valid moves the game is over and the score of the second soldier is equal to the number of rounds he performed.
To make the game more interesting, first soldier chooses n of form a! / b! for some positive integer a and b (a ≥ b). Here by k! we denote the factorial of k that is defined as a product of all positive integers not large than k.
What is the maximum possible score of the second soldier?
InputFirst line of input consists of single integer t (1 ≤ t ≤ 1 000 000) denoting number of games soldiers play.
Then follow t lines, each contains pair of integers a and b (1 ≤ b ≤ a ≤ 5 000 000) defining the value of n for a game.
OutputFor each game output a maximum score that the second soldier can get.
2 3 1 6 3
When you have more than 10^5 test cases and time in the range of 2-3 seconds You can be sure
Either you have to answer in log(N) But when you have 10^6 test cases It's better
to pre-calculate answers and save them and the complexity would be preprocessing+ testcase*O(1) .
a!/b! = a*(a-1)*(a-2)*.....(b+1)
#)Using sieve to calculate any prime factor of a range of numbers.
#)Calculating all prime factors of a range of numbers in O(N).
#)Storing sum of all prime factors of a range of numbers using prefix sum.