Score : $500$ points

Problem Statement

Count the pairs of length-$N$ sequences consisting of integers between $1$ and $M$ (inclusive), $A_1, A_2, \cdots, A_{N}$ and $B_1, B_2, \cdots, B_{N}$, that satisfy all of the following conditions:

• $A_i \neq B_i$, for every $i$ such that $1\leq i\leq N$.
• $A_i \neq A_j$ and $B_i \neq B_j$, for every $(i, j)$ such that $1\leq i < j\leq N$.

Since the count can be enormous, print it modulo $(10^9+7)$.

Constraints

• $1\leq N \leq M \leq 5\times10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the count modulo $(10^9+7)$.

2 2

2

$A_1=1,A_2=2,B_1=2,B_2=1$ and $A_1=2,A_2=1,B_1=1,B_2=2$ satisfy the conditions.

2 3

18

141421 356237

881613484