IEEE全球极限编程大赛10.0题目题解：给出数字N，A，B，求出A,B之间与N互质的数的和（数据范围大）

题目

题目来源 第10届IEEE极限编程大赛

https://www.hackerrank.com/contests/ieeextreme-challenges/challenges/inti-sets

In order to motivate his Peruvian students, a teacher includes words in the Quechua language in his math class.

Today, he defined a curious set for a given positive integer N. He called this set, an Inti set, and defined it as the set of all positive integer numbers that have the number 1 as their single common positive divisor with number N.

The math class about Inti sets was amazing. After class, the students try to challenge to teacher. They each ask questions like this: "Could you tell me the sum of all numbers, between A and B (inclusive), that are in the Inti set of N?"

Since the teacher is tired and he's sure that you are the best in class, he wants to know if you can help him.

Input Format

The first line of input contains an integer Q, 1 ≤ Q ≤ 20, representing the number of students. Each of the next Qlines contain three space-separated integers N, A and B, which represent a query.

Constraints

1 ≤ A ≤ B ≤ N ≤ 10^12

Output Format

The output is exactly Q lines, one per student query. For each query you need to find the sum of all numbers between A and B, that are in the Inti set of N, and print the sum modulo 1000000007.

Sample Input

2
12 5 10 
5 1 4

Sample Output

12
10

Explanation

In the sample input, Q = 2, so you have to answer two questions:

In the first question N = 12, A = 5 and B = 10. So you have to find the sum of all numbers between 5 and 10, that are in the Inti set of 12.

Inti set (