Problem Statement

Find the number of permutations $A$ of $(1,2,\dots,N)$ that satisfy the following condition. Since this value can be very large, output the remainder when it is divided by $1{,}000{,}000{,}007$.

Condition: when the following operation is performed $N-1$ times on $A$, $A_1=M$ holds.

Let $B$ be the sequence after the operation.
Operation: The length of the sequence $B$ is $( A の長さ) - 1$, and for every $i$ satisfying $1\le i\le (Aの長さ)-1$, $$ \begin{aligned}\ B_i=\begin{cases}gcd(A_i,A_{i+1})&(iが奇数) \\ lcm(A_i,A_{i+1})&(iが偶数) \end{cases}\end{aligned} $$ holds.
　　　Here, $gcd(x,y)$ denotes the greatest common divisor of $x$ and $y$, and $lcm(x,y)$ denotes the least common multiple of $x$ and $y$.

Input

$N$ $M$

$2\le N\le 10^5,1\le M\le 10^9$

Output

Output the number of permutations $A$ satisfying the condition, modulo $1{,}000{,}000{,}007$. Print a newline at the end.

Sample

3 1

6

2 1

2

3 100

0

100 30

945719957