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 C# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int MM = (int) 1e6;
		
		mlong[] fact = new mlong[MM];
		fact[0] = 1;
		for(int i=1;i<MM;i++) fact[i] = fact[i-1] * i;
		
		mlong[] finv = new mlong[MM];
		finv[MM-1] = (mlong) 1 /fact[MM-1] ;
		for(int i=MM-2;i>=1;i--) finv[i] = finv[i+1] * (i + 1);
		finv[0] = 1;
		
		Func<int,int,mlong> comb = (n, k) => fact[n] * finv[k] * finv[n - k];
		Func<int,int,mlong> perm = (n, k) => fact[n] * finv[n - k];
		
		mlong[] cnt = new mlong[N + 1];
		for(int i=0;i<=N;i++){
			mlong c = perm(M - i, N - i) * perm(M - i, N - i) * comb(N, i) * perm(M, i);
			cnt[i] = c;
		}
		
		mlong ans = 0;
		mlong sig = 1;
		for(int i=0;i<=N;i++){
			ans += sig * cnt[i];
			sig *= -1;
		}
		
		Console.WriteLine(ans);
		
		
		
	}
	int N,M;
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1];
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}


struct mlong {
	
	const long mod = (long) 1e9 + 7;
	long V;
	
	public mlong(long _v = 0){
		V = _v;
	}
	
	public static mlong operator+(mlong a, mlong b){
		var v0 = a.V + b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator-(mlong a, mlong b){
		var v0 = mod + a.V - b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator-(mlong b){
		var v0 = mod - b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator*(mlong a, mlong b){
		var v0 = a.V * b.V; if(v0 >= mod) v0 %= mod;
		return new mlong(v0);
	}
	public static mlong operator/(mlong a, mlong b){
		var v0 = a.V * inv(b.V).V; if(v0 >= mod) v0 %= mod;
		return new mlong(v0);
	}
	
	
	public static mlong inv(long x){
		long a = 0, b = 0, c = 0;
		ExtGCD(x, mod, ref a, ref b, ref c);
		return (mlong)((a + mod) % mod);
	}
	
	public static void ExtGCD(long x, long y, ref long a, ref long b, ref long c){
		long r0 = x; long r1 = y;
		long a0 = 1; long a1 = 0;
		long b0 = 0; long b1 = 1;
		long q1, r2, a2, b2;
		while(r1 > 0){
			q1 = r0 / r1;
			r2 = r0 % r1;
			a2 = a0 - q1 * a1;
			b2 = b0 - q1 * b1;
			r0 = r1; r1 = r2;
			a0 = a1; a1 = a2;
			b0 = b1; b1 = b2;
		}
		c = r0;
		a = a0;
		b = b0;
	}
	
	public static mlong ModPow(mlong a, long k){
		if(k == 0) return (mlong) 1;
		if(a == 0) return (mlong) 0;
		mlong x = a;
		mlong ret = 1;
		while(k > 0){
			if(k % 2 == 1) ret *= x;
			x *= x;
			k >>= 1;
		}
		return ret;
	}
	
	
	public static bool operator == (mlong a, mlong b){
		 return a.Equals(b);
	}
	public static bool operator != (mlong a, mlong b){
		 return !(a == b);
	}
	
	public override bool Equals(System.Object obj){
		if(obj  ==  null) return false;
		mlong p  =  (mlong) obj;
		if((System.Object) p  ==  null) return false;
		return p.V  ==  V;
	}
	public override int GetHashCode(){
		return V.GetHashCode();
	}
	
	public static implicit operator mlong(long n){
		long v = n % mod; if(v < 0) v += mod;
		return new mlong(v);
	}
	public static implicit operator mlong(int n){
		long v = n % mod; if(v < 0) v += mod;
		return new mlong(v);
	}
	public static explicit operator long(mlong n){
		return n.V;
	}
	
	public override String ToString(){
		return V.ToString();
	}
	
	
}