BestCoder Round #6（1003）hdu4983（欧拉函数）

Goffi and GCD

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 412    Accepted Submission(s): 34

Problem Description

Goffi is doing his math homework and he finds an equality on his text book: gcd(n−a,n)×gcd(n−b,n)=nk.

Goffi wants to know the number of (a,b) satisfy the equality, if n and k are given and 1≤a,b≤n.

Note: gcd(a,b) means greatest common divisor of a and b.

 

Input

Input contains multiple test cases (less than 100). For each test case, there's one line containing two integers n and k (1≤n,k≤109).

 

Output

For each test case, output a single integer indicating the number of (a,b) modulo 109+7.

 

Sample Input

2 13 2

 

Sample Output

21
Hint
For the first case, (2, 1) and (1, 2) satisfy the equality.

题意：RT

思路：很容易看出k>2时无解，k=2时一个解，k=1时可以预处理出G（x），表示gcd(i,n)=x的i的个数，这里求G（x）等价于求小于n/x且与之互素的数的个数，然后最后累加

            G（x）*G（n/x）即可，其中x是n的因子