D. Unusual Sequences (数论,质因子分解,dp)

D. Unusual Sequences

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Count the number of distinct sequences a1, a2, ..., an (1 ≤ ai) consisting of positive integers such that gcd(a1, a2, ..., an) = x and . As this number could be large, print the answer modulo 109 + 7.

gcd here means the greatest common divisor.

Input

The only line contains two positive integers x and y (1 ≤ x, y ≤ 109).

Output

Print the number of such sequences modulo 109 + 7.

Examples

input

Copy

3 9

output

Copy

3

input

Copy

5 8

output

Copy

0

Note

There are three suitable sequences in the first test: (3, 3, 3), (3, 6), (6, 3).

There are no suitable sequences in the second test.

题意:构造数列使得gcd(a1,a2,...,an)=n && a1+a2+...+an=m 询问共有多少种构造方法。

题解:首先可知m%n必须为0,否则无法构造,此时可分出m/n个n,利用隔板法可得共有qpow(2,m/n-1)种方案,然后再将 gcd==k*n 的方案减去即可。

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