Problem:
Problem Statement

You are given two integers a and b (a≤b). Determine if the product of the integers a, a+1, …, b is positive, negative or zero.

Constraints

a and b are integers.

-10^9≤a≤b≤10^9

Partial Score

In test cases worth 100 points, -10≤a≤b≤10.

Input

The input is given from Standard Input in the following format:

a b

Output

If the product is positive, print Positive. If it is negative, print Negative. If it is zero, print Zero.

Sample Input 1

1 3

Sample Output 1

Positive

1×2×3=6 is positive.

Sample Input 2

-3 -1

Sample Output 2

Negative

(-3)×(-2)×(-1)=-6 is negative.

Sample Input 3

-1 1

Sample Output 3

Zero

(-1)×0×1=0.

Solution in Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
from math import factorial, fabs
a, b = map(int, input().split())
try:
    if factorial(b)/factorial(a)==0:
        print("Zero")
        sys.exit()
except:
    if 0 in range(a, b+1):
        print("Zero")
        sys.exit()       
    c=0
x=True
if (fabs(a)-fabs(b))%2==0 and (b<0):
    x=False
a, b= fabs(a), fabs(b)
fin=int(factorial(b)/factorial(a))
if fin==0 and factorial(b)/factorial(a)!=0:
    fin=int(factorial(a)/factorial(b))
if x==False:
    fin*=-1
if fin==0:
    ans="Zero"
elif fin<0:
    ans="Negative"
else:
    ans="Positive"
print(ans)