NEQ

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N M

outputFormat

Output

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

Examples

Input

2 2

Output

2

Input

2 3

Output

18

Input

141421 356237

Output

881613484

样例

141421 356237

881613484