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 Ruby (2.3.3) (judge verdict: Runtime Error)

MOD=(10**9)+7
$fac=[]
$finv=[]
$inv=[]
$fac[0] = 1
$fac[1] = 1
$inv[0] = 1
$finv[1] = 1
$inv[1] = 1
for i in 2..1000000
  $fac[i] = $fac[i - 1] * i % MOD
  $inv[i] = MOD - $inv[MOD%i] * (MOD / i) % MOD
  $finv[i] = $finv[i - 1] * $inv[i] % MOD
end

def com(n,k)
  return 0 if n<k
  return 0 if(n<0 || k<0)
  return $fac[n] * ($finv[k] * $finv[n - k] % MOD) % MOD;
end



x,y=gets.chomp.split(" ").map{|s| s.to_i}
if (x+y)%3!=0
  p 0
  exit
end

u=[x,y].max
v=[x,y].min
c=0
while u!=v
  u-=2
  v-=1
  c+=1
end
p=u/3
a=[]
a[0]=1

p com(c+p*2,p)%MOD