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).

-----Sample Input-----
2 2

-----Sample Output-----
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.

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