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).

Input

Input is given from Standard Input in the following format:
N M

Output

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

Constraints

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

Sample Input 1

2 2

Sample Output 1

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.

Sample Input 2

2 3

Sample Output 2

18

Sample Input 3

141421 356237

Sample Output 3

881613484

见题面 Input 部分

见题面 Output 部分