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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<math.h>
#define X 1000000007
long fact[2000001] = {};
long invfact[2000001] = {};

long pow_(long a,long n){
  long ans = 1;
  while(n>0){
    if(n & 1){
      ans = (ans * a) % X;
    }
    a = (a * a) % X;
    n >>= 1;
  }
  return ans;
}
  
void makefact(){
  long i = 1;
  for(i=1;i<=2000000;i++){
    if(i==1){
      fact[i] = 1;
      invfact[i] = 1;
    }else{
      fact[i] = (fact[i-1] * i) % X;
      invfact[i] = pow_(fact[i],X-2) % X;
    }
  }
}

int main(){
  long x = 0;
  long y = 0;
  long movea = 0;
  long moveb = 0;
  long i = 0;
  long j = 0;
  long oh = 0;
  
  scanf("%ld %ld",&x,&y);
  makefact();
  for(i = 0;i < x/2+1;i++){
    movea = x - 2 * i;
    moveb = i;
    if(2*movea + moveb == y){
      //printf("%ld %ld/",movea,moveb);
      break;
    }
  }
  //printf("%ld/",(fact[200]*invfact[200])%X);
  oh = ((fact[movea+moveb]*invfact[movea])%X)*invfact[moveb];
  oh = oh % 1000000007;
  printf("%ld",oh);
  return 0;
}