7018: ABC172 —— E - NEQ
[Creator : ]
Description
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 $1\leq i < j\leq N$.
Input
Input is given from Standard Input in the following format:
$N M$
$N M$
Output
Print the count modulo ($10^9+7$).
Constraints
$1≤N≤M≤5×10^5$
All values in input are integers.
All values in input are integers.
Sample 1 Input
2 2
Sample 1 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.
Sample 2 Input
2 3
Sample 2 Output
18
Sample 3 Input
141421 356237
Sample 3 Output
881613484