Buggy python submission (verdict: Time Limit Exceeded):
x,y=map(int,input().split())
T=x+y
W=x-T//3
D=10**9
#print(T//3)

import sys
if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()

if x==y==999999:
    print(151840682)
    sys.exit()

from functools import lru_cache
@lru_cache(maxsize=100000000)
def c(n,k): 
  return 1 if(k<=0 or n<=k) else (c(n-1, k-1) + c(n-1, k))%D

sys.setrecursionlimit(100000000)
print(c(T//3,W))


Fixed submission:
import sys

x,y=map(int,input().split())
T=x+y
MOD=10**9+7

def nCmMOD(A,B,Mod):
    num,den=1,1
    for i in range(B):
        num*=(A-i)
        den*=(i+1)
        num%=Mod
        den%=Mod
    return (num*pow(den,Mod-2,Mod))%Mod

if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()
else:
    n=(2*y-x)//3
    m=(2*x-y)//3
    l=min(n,m)
    print(nCmMOD(n+m,l,MOD))

Buggy python submission (verdict: Runtime Error):
x,y=map(int,input().split())
T=x+y
W=x-T//3
D=10**9
#print(T//3)

import sys
if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()

if x==y==999999:
    print(151840682)
    sys.exit()

from functools import lru_cache
@lru_cache(maxsize=1000000)
def c(n,k): 
  return 1 if(k<=0 or n<=k) else (c(n-1, k-1) + c(n-1, k))%D

sys.setrecursionlimit(1000000)
print(c(T//3,W))


Fixed submission:
import sys

x,y=map(int,input().split())
T=x+y
MOD=10**9+7

def nCmMOD(A,B,Mod):
    num,den=1,1
    for i in range(B):
        num*=(A-i)
        den*=(i+1)
        num%=Mod
        den%=Mod
    return (num*pow(den,Mod-2,Mod))%Mod

if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()
else:
    n=(2*y-x)//3
    m=(2*x-y)//3
    l=min(n,m)
    print(nCmMOD(n+m,l,MOD))

Buggy python submission (verdict: Runtime Error):
x,y=map(int,input().split())
T=x+y
W=x-T//3
D=10**9
#print(T//3)

import sys
if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()

if x==y==999999:
    print(151840682)
    sys.exit()

from functools import lru_cache
@lru_cache(maxsize=1000000)
def c(n,k): 
  return 1 if(k<=0 or n<=k) else (c(n-1, k-1) + c(n-1, k))%D

sys.setrecursionlimit(10000)
print(c(T//3,W))

Fixed submission:
import sys

x,y=map(int,input().split())
T=x+y
MOD=10**9+7

def nCmMOD(A,B,Mod):
    num,den=1,1
    for i in range(B):
        num*=(A-i)
        den*=(i+1)
        num%=Mod
        den%=Mod
    return (num*pow(den,Mod-2,Mod))%Mod

if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()
else:
    n=(2*y-x)//3
    m=(2*x-y)//3
    l=min(n,m)
    print(nCmMOD(n+m,l,MOD))

Buggy python submission (verdict: Runtime Error):
x,y=map(int,input().split())
T=x+y
W=x-T//3
D=10**9
print(T//3)

import sys
if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()

if x==y==999999:
    print(151840682)
    sys.exit()

from functools import lru_cache
@lru_cache(maxsize=1000000)
def c(n,k): 
  return 1 if(k<=0 or n<=k) else (c(n-1, k-1) + c(n-1, k))%D

sys.setrecursionlimit(10000)
print(c(T//3,W))

Fixed submission:
import sys

x,y=map(int,input().split())
T=x+y
MOD=10**9+7

def nCmMOD(A,B,Mod):
    num,den=1,1
    for i in range(B):
        num*=(A-i)
        den*=(i+1)
        num%=Mod
        den%=Mod
    return (num*pow(den,Mod-2,Mod))%Mod

if T%3!=0 or y/x<1/2 or y/x>2:
    print(0)
    sys.exit()
else:
    n=(2*y-x)//3
    m=(2*x-y)//3
    l=min(n,m)
    print(nCmMOD(n+m,l,MOD))