Problem Statement

Snuke has a die (singular of dice) that shows integers from $1$ through $N$ with equal probability, and an integer $1$. He repeats the following operation while his integer is less than or equal to $M$.

• He rolls the die. If the die shows an integer $x$, he multiplies his integer by $x$.

Find the expected value of the number of times he rolls the die until he stops, modulo $10^9+7$.

Definition of the expected value modulo $10^9+7$ We can prove that the desired expected value is always a rational number. Moreover, under the constraints of the problem, when the value is represented as an irreducible fraction $\frac{P}{Q}$, we can also prove that $Q \not\equiv 0 \pmod{10^9+7}$. Thus, an integer $R$ such that $R \times Q \equiv P \pmod{10^9+7}$ and $0 \leq R \lt 10^9+7$ is uniquely determined. Answer such $R$.

Constraints

• $2 \leq N \leq 10^9$
• $1 \leq M \leq 10^9$

Input

Input is given from Standard Input in the following format:

N M

Output

Print the answer.