Problem: Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.  Let us define a function f(r, c) as follows:    * f(r,c) :=  (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)  Given are integers r_1, r_2, c_1, and c_2. Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Submission attempts (in order):
import sys
input = sys.stdin.buffer.readline
 
def main():
    a,b,c,d = map(int,input().split())
    MOD = 10**9+7
    K= c+d+5
    fac = [0 for i in range(K+1)]
    fac[0],fac[1] = 1,1
 
    for i in range(2,K+1):
        fac[i] = (fac[i-1]*i)%MOD
        
    def comb(e,f):
        return (fac[e+f]*pow(fac[e],MOD-2,MOD)*pow(fac[f],MOD-2,MOD))%MOD
 
    print((comb(c+1,d+1)-comb(c+1,b)-comb(d+1,a)+comb(a,b))%MOD)
    
if _name_ == "_main_":
    main()
#print the result

import sys
input = sys.stdin.buffer.readline
 
def main():
    a,b,c,d = map(int,input().split())
    MOD = 10**9+7
    K= c+d+5
    fac = [0 for _ in range(K+1)]
    fac[0],fac[1] = 1,1
 
    for i in range(2,K+1):
        fac[i] = (fac[i-1]*i)%MOD
        
    def comb(e,f):
        return (fac[e+f]*pow(fac[e],MOD-2,MOD)*pow(fac[f],MOD-2,MOD))%MOD
 
    print((comb(c+1,d+1)-comb(c+1,b)-comb(d+1,a)+comb(a,b))%MOD)
    
if _name_ == "_main_":
    main()
#print the result

import sys
input = sys.stdin.buffer.readline
 
def main():
    a,b,c,d = map(int,input().split())
    MOD = 10**9+7
    N = c+d+5
    fac = [0 for _ in range(N+1)]
    fac[0],fac[1] = 1,1
 
    for i in range(2,N+1):
        fac[i] = (fac[i-1]*i)%MOD
        
    def comb(x,y):
        return (fac[x+y]*pow(fac[x],MOD-2,MOD)*pow(fac[y],MOD-2,MOD))%MOD
 
    print((comb(c+1,d+1)-comb(c+1,b)-comb(d+1,a)+comb(a,b))%MOD)
    
if _name_ == "_main_":
    main()

def findTrailingZeros(n): 

      

    # If n is odd 

    if (n & 1): 

        return 0

  

    # If n is even 

    else: 

        ans = 0

  

        # Find the trailing zeros 

        # in n/2 factorial 

        n //= 2

        while (n): 

            ans += n // 5

            n //= 5

  

        # Return the required answer 

        return ans 

  
# Driver code 

  

n = 12

  

print(findTrailingZeros(n))

import sys
input = sys.stdin.buffer.readline
 
def main():
    a,b,c,d = map(int,input().split())
    MODE = 10**9+7
    NU = c+d+5
    fac = [0 for _ in range(NU+1)]
    fac[0],fac[1] = 1,1
 
    for i in range(2,NU+1):
        fac[i] = (fac[i-1]*i)%MODE
        
    def comb(x,y):
        return (fac[x+y]*pow(fac[x],MODE-2,MODE)*pow(fac[y],MODE-2,MODE))%MODE
 
    print((comb(c+1,d+1)-comb(c+1,b)-comb(d+1,a)+comb(a,b))%MODE)
    
if _name_ == "_main_":
    main()

import sys
input = sys.stdin.buffer.readline
 
def main():
    a,b,c,d = map(int,input().split())
    MOD = 10**9+7
    P= c+d+5
    fac = [0 for _ in range(P+1)]
    fac[0],fac[1] = 1,1
 
    for i in range(2,P+1):
        fac[i] = (fac[i-1]*i)%MOD
        
    def comb(x,y):
        return (fac[x+y]*pow(fac[x],MOD-2,MOD)*pow(fac[y],MOD-2,MOD))%MOD
 
    print((comb(c+1,d+1)-comb(c+1,b)-comb(d+1,a)+comb(a,b))%MOD)
    
if _name_ == "_main_":
    main()


import sys
import math
input = sys.stdin.buffer.readline
 
def main():
    a,b,c,d = map(int,input().split())
    MOD = 10**9+7
    N = c+d+5
    fac = [0 for _ in range(N+1)]
    fac[0],fac[1] = 1,1
 
    for i in range(2,N+1):
        fac[i] = (fac[i-1]*i)%MOD
        
    def comb(x,y):
        return (fac[x+y]*pow(fac[x],MOD-2,MOD)*pow(fac[y],MOD-2,MOD))%MOD
 
    print((comb(c+1,d+1)-comb(c+1,b)-comb(d+1,a)+comb(a,b))%MOD)
    
if __name__ == "__main__":
    main()

Verdicts: Runtime Error

Runtime Error

Runtime Error

Wrong Answer

Runtime Error

Runtime Error

Accepted