Problem:
Score : 400 points

Problem Statement

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

1 \leq X \leq 10^6

1 \leq Y \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.PrintStream;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws Exception{
		new Main(new Scanner(System.in), System.out, System.err).exec();
	}
	public final Scanner sc;
	public final PrintStream out, err;
	public Main(final Scanner sc, final PrintStream out, final PrintStream err) {
		this.sc = sc;this.out = out;this.err = err;
	}
	static private final long pair(int a, int b) {return (((long)a) << 32) + b;}
	static private final int upper(long v) {return (int)(v >> 32);}
	static private final int lower(long v) {return (int)(v & 0xFFFFFFFF);}

	//-----------------------------------------

	static public final long load(int end, int length) {
		return pair(end, length);
	}
	static public final int end(long load) {
		return upper(load);
	}
	static public final int length(long load) {
		return lower(load);
	}
	static public final long score(int count, int last) {
		return pair(count, last);
	}
	static public final int count(long score) {
		return upper(score);
	}
	static public final int last(long score) {
		return lower(score);
	}

	//------------------------------------------

	private int p;
	private int[] inv;
	private int[] fact;
	private int[] finv;
	public final int mod(long v) {
		v %= p;
		return (int)(v < 0 ? v+p : v);
	}
	public final int mul(long a, long b) {
		return mod(a*b);
	}
	public final void initFact(double limit, double p) {
		initFact((int)limit, (int)p);
	}
	public final void initFact(int limit, int p) {
		this.p = p;
		this.inv = new int[limit+1];
		this.fact = new int[limit+1];
		this.finv = new int[limit+1];
		fact[1] = finv[1] = inv[0] = inv[1] = 1;
		for(int i=2;i<=limit;i++) {
			int a = p / i;
			int b = p % i;
			inv[i]  = mul(-a, inv[b]);
			fact[i] = mul(fact[i-1], i);
			finv[i] = mul(finv[i-1], inv[i]);
		}
	}
	public final int comb(int m, int n) {
		return mul(mul(fact[m], finv[n]), finv[m-n]);
	}

	//------------------------------------------

	public void exec() throws Exception{
		final int X = sc.nextInt();
		final int Y = sc.nextInt();

		if((X+Y)%3 != 0) {
			out.println(0);
			return;
		}

		int m = (2*X-Y)/3;
		int n = (2*Y-X)/3;
		if(m<0 || n<0) {
			out.println(0);
			return;
		}
		if(m==0 || n==0) {
			out.println(1);
			return;
		}
		initFact(1e6, 1e9+7);
		out.println(comb(m+n, n));
	}
}