Buggy python submission (verdict: Time Limit Exceeded):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
from math import floor
P = int(1e9)+7
def c(n, m, P):
       ch = 1
       for i in range(m):
           ch *= (n-i)
           ch %= P
       b = factorial(m) 
       b = pow(b, P-2, P)
       return ch*b%P
def main():
    x, y = map(int, readline().split())
    a = (2*y-x)/3
    b = (2*x-y)/3
    if (a < 0) or (b < 0):
        print(0)
        return
    if floor(a)-a != 0: 
        print(0)
        return
    if floor(b)-b != 0:
        print(0)
        return

    a = int(a)
    b = int(b)
    print(c(a+b, a, P)) 
if __name__ == '__main__':
    main()


Fixed submission:
#python3
from math import factorial
from math import floor
MOD = int(1e9+7)

def comb(n, m, mod):
    comb_a = 1
    for i in range(m): 
        comb_a *= (n-i)
        comb_a %= mod
    comb_tmp = factorial(m) 
    comb_b = pow(comb_tmp, mod-2, mod)
    return (comb_a * comb_b)%mod
def main():
    x, y = map(int, input().split())
    k = (2*x-y)/3
    l = (2*y-x)/3

    if floor(k) - k != 0:
        print(0)
        return
    if floor(l) - l != 0:
        print(0)
        return 
    if k<0:
        print(0)
        return
    if l<0:
        print(0)
        return
    k = int(k)
    l = int(l)
    print(comb(k+l, k, MOD)%MOD) 

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
P = int(1e9)+7
def c(n, m, P):
       ch = 1
       for i in range(m):
           ch *= (n-i)
           ch %= P
       b = factorial(m) 
       b = pow(b, P-2, P)
       return ch*b%P
def main():
    x, y = map(int, readline().split())
    a = 2*y-x
    b = 2*x-y
    if (a%3) or (b%3):
        print(0)
        return
    a = a//3
    b = b//3
    if a < 0:
        print(0)
        return
    if b < 0:
        print(0)
        return
    print(c(a+b, a, P)) 
if __name__ == '__main__':
    main()


Fixed submission:
#python3
from math import factorial
from math import floor
MOD = int(1e9+7)

def comb(n, m, mod):
    comb_a = 1
    for i in range(m): 
        comb_a *= (n-i)
        comb_a %= mod
    comb_tmp = factorial(m) 
    comb_b = pow(comb_tmp, mod-2, mod)
    return (comb_a * comb_b)%mod
def main():
    x, y = map(int, input().split())
    k = (2*x-y)/3
    l = (2*y-x)/3

    if floor(k) - k != 0:
        print(0)
        return
    if floor(l) - l != 0:
        print(0)
        return 
    if k<0:
        print(0)
        return
    if l<0:
        print(0)
        return
    k = int(k)
    l = int(l)
    print(comb(k+l, k, MOD)%MOD) 

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
P = int(1e9)+7
def c(n, m, P):
       ch = 1
       for i in range(m):
           ch *= (n-i)
           ch %= P
       b = factorial(m) 
       b = pow(b, P-2, P)
       return ch*b%P
def main():
    x, y = map(int, readline().split())
    if ((2*y-x)%3) or ((2*x-y)%3):
        print(0)
        return
    a = (2*y-x)//3
    b = (2*x-y)//3
    if a < 0:
        print(0)
        return
    if b < 0:
        print(0)
        return
    print(c(a+b, a, P)) 
if __name__ == '__main__':
    main()


Fixed submission:
#python3
from math import factorial
from math import floor
MOD = int(1e9+7)

def comb(n, m, mod):
    comb_a = 1
    for i in range(m): 
        comb_a *= (n-i)
        comb_a %= mod
    comb_tmp = factorial(m) 
    comb_b = pow(comb_tmp, mod-2, mod)
    return (comb_a * comb_b)%mod
def main():
    x, y = map(int, input().split())
    k = (2*x-y)/3
    l = (2*y-x)/3

    if floor(k) - k != 0:
        print(0)
        return
    if floor(l) - l != 0:
        print(0)
        return 
    if k<0:
        print(0)
        return
    if l<0:
        print(0)
        return
    k = int(k)
    l = int(l)
    print(comb(k+l, k, MOD)%MOD) 

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
P = int(1e9)+7
def c(n, m):
       ch = 1
       for i in range(m):
           ch *= (n-i)
           ch %= P
       b = factorial(m) 
       b = pow(b, P-2, P)
       return ch*b%P
def main():
    x, y = map(int, readline().split())
    if ((2*y-x)%3) or ((2*x-y)%3):
        print(0)
        return
    a = (2*y-x)//3
    b = (2*x-y)//3
    if a < 0:
        print(0)
        return
    if b < 0:
        print(0)
        return
    print(c(a+b, a)) 
if __name__ == '__main__':
    main()


Fixed submission:
#python3
from math import factorial
from math import floor
MOD = int(1e9+7)

def comb(n, m, mod):
    comb_a = 1
    for i in range(m): 
        comb_a *= (n-i)
        comb_a %= mod
    comb_tmp = factorial(m) 
    comb_b = pow(comb_tmp, mod-2, mod)
    return (comb_a * comb_b)%mod
def main():
    x, y = map(int, input().split())
    k = (2*x-y)/3
    l = (2*y-x)/3

    if floor(k) - k != 0:
        print(0)
        return
    if floor(l) - l != 0:
        print(0)
        return 
    if k<0:
        print(0)
        return
    if l<0:
        print(0)
        return
    k = int(k)
    l = int(l)
    print(comb(k+l, k, MOD)%MOD) 

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
def main():
    x, y = map(int, readline().split())
    if ((2*y-x)%3) or ((2*x-y)%3):
        print(0)
        return
    a = (2*y-x)//3
    b = (2*x-y)//3
    if a < 0:
        print(0)
        return
    if b < 0:
        print(0)
        return
    P = int(1e9)+7
    def c(n, m):
        ch = 1
        for i in range(m):
            ch *= (n-i)
            ch %= P
        b_ = factorial(m) 
        b = pow(b_, P-2, P)
        return ch*b%P
    print(c(a+b, a)) 
if __name__ == '__main__':
    main()


Fixed submission:
#python3
from math import factorial
from math import floor
MOD = int(1e9+7)

def comb(n, m, mod):
    comb_a = 1
    for i in range(m): 
        comb_a *= (n-i)
        comb_a %= mod
    comb_tmp = factorial(m) 
    comb_b = pow(comb_tmp, mod-2, mod)
    return (comb_a * comb_b)%mod
def main():
    x, y = map(int, input().split())
    k = (2*x-y)/3
    l = (2*y-x)/3

    if floor(k) - k != 0:
        print(0)
        return
    if floor(l) - l != 0:
        print(0)
        return 
    if k<0:
        print(0)
        return
    if l<0:
        print(0)
        return
    k = int(k)
    l = int(l)
    print(comb(k+l, k, MOD)%MOD) 

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
def main():
    x, y = map(int, readline().split())
    if ((2*y-x)%3) or ((2*x-y)%3):
        print(0)
        return
    a = (2*y-x)//3
    b = (2*x-y)//3
    if a < 0:
        print(0)
        return
    if b < 0:
        print(0)
        return
    P = int(1e9)+7
    def c(n, m):
        ch = 1
        for i in range(m):
            ch *= (n-i)
            ch %= P
        b = factorial(m) 
        b = pow(b, P-2, P)
        return ch*b%P
    print(c(a+b, a)) 
if __name__ == '__main__':
    main()


Fixed submission:
#python3
from math import factorial
from math import floor
MOD = int(1e9+7)

def comb(n, m, mod):
    comb_a = 1
    for i in range(m): 
        comb_a *= (n-i)
        comb_a %= mod
    comb_tmp = factorial(m) 
    comb_b = pow(comb_tmp, mod-2, mod)
    return (comb_a * comb_b)%mod
def main():
    x, y = map(int, input().split())
    k = (2*x-y)/3
    l = (2*y-x)/3

    if floor(k) - k != 0:
        print(0)
        return
    if floor(l) - l != 0:
        print(0)
        return 
    if k<0:
        print(0)
        return
    if l<0:
        print(0)
        return
    k = int(k)
    l = int(l)
    print(comb(k+l, k, MOD)%MOD) 

main()

Buggy python submission (verdict: Runtime Error):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

from math import factorial 
def main():
    x, y = map(int, readline().split())
    if ((2*y-x)%3) or ((2*x-y)%3):
        print(0)
        return
    a = (2*y-x)//3
    b = (2*x-y)//3
    P = int(1e9)+7
    def c(n, m):
        ch = 1
        for i in range(m):
            ch *= (n-i)
            ch %= P
        b = factorial(m) 
        b = pow(b, P-2, P)
        return ch*b%P
    print(c(a+b, a)) 
if __name__ == '__main__':
    main()


Fixed submission:
#python3
from math import factorial
from math import floor
MOD = int(1e9+7)

def comb(n, m, mod):
    comb_a = 1
    for i in range(m): 
        comb_a *= (n-i)
        comb_a %= mod
    comb_tmp = factorial(m) 
    comb_b = pow(comb_tmp, mod-2, mod)
    return (comb_a * comb_b)%mod
def main():
    x, y = map(int, input().split())
    k = (2*x-y)/3
    l = (2*y-x)/3

    if floor(k) - k != 0:
        print(0)
        return
    if floor(l) - l != 0:
        print(0)
        return 
    if k<0:
        print(0)
        return
    if l<0:
        print(0)
        return
    k = int(k)
    l = int(l)
    print(comb(k+l, k, MOD)%MOD) 

main()