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 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).

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

2 1
3 2

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