Problem:
Score : 500 points

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).

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 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

Solution in Python (3.8.2) (judge verdict: Runtime Error)

M=10**9+7
n,m=map(int,input().split())
import sys, functools as ft
sys.setrecursionlimit(10**9)
@ft.lru_cache(None)
def f(n):
  if n<2: return 1
  return n*f(n-1)%M
a=0
for k in range(n+1):
  a+=(-1)**k*f(m-k)*pow(f(k)*f(n-k),-1,M)%M
print(a*f(n)*f(m)*pow(f(m-n)**2,-1,M)%M)