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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
#define INF 0x3f3f3f3f3f3f3f3f
#define MOD 1000000007
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define foreach(i, v) for (__typeof((v).begin()) i = (v).begin(); i != (v).end(); ++ i)
const double pi = acos(-1.0);

// (0,0)->(x,y)
// each +3
//
//

// 2,1 -> XXY XYX YXX;
//
ll inv[1000010];
void initinv(){
  ll p = MOD;
  inv[1] = 1;
  rep(i,2,1000001)
    inv[i] = ((p-p/i)*inv[p%i])%p;
}

int main(){
  initinv();
  ll x,y;
  scanf("%lld %lld",&x,&y);
  if((x+y)%3){
    printf("0\n");
    return 0;
  }
  int times = (x+y)/3;
  x-=times;
  y-=times;
  if(x<0 || y < 0){
    printf("0\n");
    return 0;
  }
  if(x==0 || y ==0){
    printf("1\n");
    return 0;
  }

  // inv;
  // (x+y)!/(x)!/(y)!;
  //
  ll ans=1;
  rep(i,x+1,x+y+1){
    (ans*=i)%=MOD;
  }
  rep(i,1,y+1){
    (ans*=inv[i])%=MOD;
  }
  cout<<(ans+MOD)%MOD<<endl;
  return 0;
}