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).

Examples

Input

2 2

Output

2

Input

2 3

Output

18

Input

141421 356237

Output

881613484

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见题面