Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 != 0:
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)


Fixed submission:
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 or not (X <= 2*Y and Y <= 2*X):
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 != 0:
    print(0)
    exit()

x_tmp=X
y_tmp=Y

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)


Fixed submission:
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 or not (X <= 2*Y and Y <= 2*X):
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 != 0:
    print(0)
    exit()

x_tmp=X
y_tmp=Y

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,y_count,mod)
print(ret)


Fixed submission:
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 or not (X <= 2*Y and Y <= 2*X):
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)

Buggy python submission (verdict: Runtime Error):
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 != 0:
    print(0)
    exit()

x_tmp=X
y_tmp=Y

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,y_count,mod)
print(ret)


Fixed submission:
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 or not (X <= 2*Y and Y <= 2*X):
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 != 0:
    print(0)
    exit()

x_tmp=X
y_tmp=Y

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
N = sum
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(N,x_count,mod)
print(ret)


Fixed submission:
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 or not (X <= 2*Y and Y <= 2*X):
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 != 0:
    print(0)
    exit()

x_tmp=X
y_tmp=Y

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
N = sum
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(N,x_count,mod)
print(ret)


Fixed submission:
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 or not (X <= 2*Y and Y <= 2*X):
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)

Buggy python submission (verdict: Runtime Error):
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 != 0:
    print(0)
    exit()

x_tmp=X
y_tmp=Y

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2

sum = x_count + y_count

def cmb(n,r):
    r = min(n-r,r)
    if r == 0: return 1
    over = reduce(mul, range(n, n - r, -1))
    under = reduce(mul, range(1,r + 1))
    return over // under

ret = cmb(sum, x_count) % (10**9+7)
print(ret)


Fixed submission:
from operator import mul
from functools import reduce

X,Y = map(int,input().split()[:2])

if (X + Y) % 3 or not (X <= 2*Y and Y <= 2*X):
    print(0)
    exit()

x_tmp=X+1
y_tmp=Y+2

x_count=0
y_count=0

while x_tmp*2 != y_tmp:
    x_tmp-=2
    y_tmp-=1
    x_count+=1

y_count = y_tmp//2 - 1

sum = x_count + y_count

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

for i in range( 2, sum + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

ret = cmb(sum,x_count,mod)
print(ret)