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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local mod = 1000000007

local function bmul(x, y)
  return (x * y) % mod
end

local function badd(x, y)
  return (x + y) % mod
end

local function bsub(x, y)
  return x < y and x - y + mod or x - y
end

local function modpow(src, pow)
  local res = 1
  while 0 < pow do
    if pow % 2 == 1 then
      res = bmul(res, src)
      pow = pow - 1
    end
    src = bmul(src, src)
    pow = pow // 2
  end
  return res
end

local function modinv(src)
  return modpow(src, mod - 2)
end

local function getComb(n, k)
  local ret = 1
  local inv = 1
  for i = 1, k do
    ret = bmul(ret, n + 1 - i)
    inv = bmul(inv, i)
  end
  return bmul(ret, modinv(inv))
end

local x, y = io.read("*n", "*n")
if (x + y) % 3 ~= 0 then
  print(0) os.exit()
end
local z = (x + y) // 3
x, y = x - z, y - z
if x < 0 or y < 0 then
  print(0) os.exit()
end
print(getComb(x + y, x))