URI Online Judge | 1234

# The Goblet of Fire

By Leandro Zatesko, UFFS Brazil

Timelimit: 1

One of the trials of the Triwizard Tournament will be a football match, and Chapecoense has been training hard to face Hogwarts players. The Chapecoense Football Association (in Portuguese: Associação Chapecoense de Futebol, or shortly ACF, or simply Chapecoense) is the football team of the city of Chapecó. Founded in 1973, the team nowadays plays among the best teams of Brazil, and it is not some freak teenagers of hat and broomstick that are going to frighten our brave warriors, even though we all have been shocked when the Goblet of Fire chose our muggle players to participate of the Triwizard Tournament. As we have previously mentioned, the history of the team begins in 1973 when…

We interrupt this text for the transmission of an urgent message of the Minister of Magic.

 Good afternoon, muggle ladies and gentlemen! Cursed be the day in which Dolores Umbridge has left the prison. Now, she lives to piss me off with those Math problems. And she knows I'm not good at these things. So, can you write a program to help me? The problem is: she says to me an integer N and asks me to tell how many divisors N has and to keep this N in my head. So far so good. I'm not that stupid and I don't need help in this part. But then she keeps saying to me some prime numbers and, for each prime p she says, I'm supposed to multiply p by N, updating the value of N in my head, and, as if it were not enough, I still have to tell her how many divisors this new N has which are composed only by prime factors less than p. For example, if I have kept in my head N = 630 and she says p = 5, I must update N to 3150 and say 6, for the only divisors of 3150 composed only by prime factors less than 5 are: 1, 2, 3, 6, 9 and 18. But the number N grows very quickly, and I don't want to lose the game to her. Please do something!

## Input

The input consists of at least 2 and at most 105 lines. The first line consists of the single integer N (2 ≤ N ≤ 1012). Each one of the next lines consist of a single prime number p (2 ≤ p ≤ 107). The integers are given in the input in the order that Dolores Umbridge says them. The input ends in end of file.

## Output

For each prime number p said by Dolores Umbridge, print a line consisting only of the answer that the Minister of Magic was supposed to give her. As the answer can be a very large number, print only the remainder that is left when the answer is divided by 109 + 7.

 Input Samples Output Samples 630 5 7 2 3 11 6 18 1 3 108
 2 3 5 7 11 2 4 8 16
 2 2 2 2 3 1 1 1 5