Buggy python submission (verdict: Runtime Error):
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
N = x+y
K = min(x,y)
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [0]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [0]*(N+1)
finv[N] = pow(fact[N], mod-2, mod)
for i in range(N, 0, -1):
    finv[i-1] = (finv[i]*i) %mod

print((fact[x+y]*finv[x]*finv[y]) % mod)

Fixed submission:
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
if x < 0 or y < 0:
    print(0)
    exit(0)
N = x+y
K = min(x,y)
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [0]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [0]*(N+1)
finv[N] = pow(fact[N], mod-2, mod)
for i in range(N, 0, -1):
    finv[i-1] = (finv[i]*i) %mod
print((fact[x+y]*finv[x]*finv[y]) % mod)

Buggy python submission (verdict: Runtime Error):
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
N = x+y
K = min(x,y)
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [None]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [None]*(N+1)
finv[N] = pow(fact[N], mod-2, mod)
for i in range(N, 0, -1):
    finv[i-1] = (finv[i]*i) %mod
def comb(n, k):
    return (fact[n]*finv[n-k]*finv[k]) % mod
print(comb(N,K))

Fixed submission:
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
if x < 0 or y < 0:
    print(0)
    exit(0)
N = x+y
K = min(x,y)
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [0]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [0]*(N+1)
finv[N] = pow(fact[N], mod-2, mod)
for i in range(N, 0, -1):
    finv[i-1] = (finv[i]*i) %mod
print((fact[x+y]*finv[x]*finv[y]) % mod)

Buggy python submission (verdict: Runtime Error):
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
N = x+y
K = x
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [None]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [None]*(N+1)
finv[-1] = pow(fact[-1], mod-2, mod)
for i in range(N, 0, -1):
    finv[i-1] = (finv[i]*i) %mod
def comb(n, k):
    return (fact[n]*finv[n-k]*finv[k]) % mod
print(comb(N,K))

Fixed submission:
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
if x < 0 or y < 0:
    print(0)
    exit(0)
N = x+y
K = min(x,y)
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [0]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [0]*(N+1)
finv[N] = pow(fact[N], mod-2, mod)
for i in range(N, 0, -1):
    finv[i-1] = (finv[i]*i) %mod
print((fact[x+y]*finv[x]*finv[y]) % mod)

Buggy python submission (verdict: Runtime Error):
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
N = x+y
K = x
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [None]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [None]*(N+1)
finv[-1] = pow(fact[-1], mod-2, mod)
for i in range(N, min(x,y)-1, -1):
    finv[i-1] = (finv[i]*i) %mod
def comb(n, k):
    return (fact[n]*finv[n-k]*finv[k]) % mod
print(comb(N,K))

Fixed submission:
X,Y = map(int,input().split())
mod = 10**9+7
if (2*X-Y) % 3 != 0 or (2*Y-X) % 3 != 0:
    print(0)
    exit(0)
x,y = (2*Y-X)//3,(2*X-Y)//3
if x < 0 or y < 0:
    print(0)
    exit(0)
N = x+y
K = min(x,y)
def pow(x, n, mod):
    ret = 1
    while n>0:
        if (n&1):
            ret = (ret*x) % mod
        x = (x*x) % mod
        n >>= 1
    return ret
fact = [0]*(N+1)
fact[0] = 1
for i in range(1, N+1):
    fact[i] = (fact[i-1]*i) % mod
finv = [0]*(N+1)
finv[N] = pow(fact[N], mod-2, mod)
for i in range(N, 0, -1):
    finv[i-1] = (finv[i]*i) %mod
print((fact[x+y]*finv[x]*finv[y]) % mod)