URI Online Judge | 2914

Looking for the Risk Factor

Por Juan Pablo Marín Rosas MX Mexico

Timelimit: 1

For testing a new cryptographic algorithm, engineers working for a large investment bank need to compute a value they named the Risk Factor of the algorithm. Informally, the Risk Factor is the amount of numbers less than or equal to a certain value N, that aren’t multiples of prime numbers greater than a certain value K.

More formally, given the values N and K, the Risk Factor is the number of elements of the following set:

{x such that 2 ≤ xN and for every prime divisor p of x, pK}

The engineers need to compute the Risk Factor for different values of N and K and have prepared a set of queries for you to answer. Can you help them?


The first line contains an integer Q (1 ≤ Q ≤ 5 × 104 ) representing the number of queries that the engineers prepared for you. Each of the following Q lines describes a query with two integers N and K (2 ≤ N, K ≤ 105 ).


Output Q lines, each line with an integer indicating the Risk Factor for the corresponding query of the input.

Exemplo de Entrada Exemplo de Saída


10 3

10 4

15 3

5 20