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 PyPy3 (7.3.0) (judge verdict: Accepted)

def cmb(n, r, mod):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return (fact[n] * factinv[r] * factinv[n-r]) % mod
mod = 10**9 + 7

fact = [1, 1]
factinv = [1, 1]
inv = [0,1]

n , m = map(int,input().split())
for i in range(2,m+1):
    fact.append((fact[-1] * i) % mod)
    inv.append((inv[mod % i] * (mod - (mod // i))) % mod)
    factinv.append((factinv[-1] * inv[-1]) % mod)

ans = 0

for i in range(0,n+1):
    ans += cmb(n,i,mod)*((-1)**i)*fact[m]*factinv[m-i]*(fact[m-i]*factinv[m-n])**2
    ans %= mod
print(ans)