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)

mod = 10**9+7
fac = [1]
fac_in = [1]
for i in range(1,5*10**5+1):
    fac.append((fac[-1]*i)%mod)
    fac_in.append((fac_in[-1]*pow(i,mod-2,mod))%mod)

def comb(a,b):
    return (fac[a]*fac_in[b]*fac_in[a-b])%mod

def perm(a,b):
    return (fac[a]*fac_in[a-b])%mod

n,m = map(int,input().split())
ans = perm(m,n)
ans1 = 0
for i in range(n+1):
    ans1 += (comb(n,i)*perm(m-i,n-i))*(-1)**i
    ans1 %= mod
ans *= ans1
print(ans%mod)