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

r1, c1, r2, c2 = [int(i) for i in input().split()]
mod = 10**9 + 7

#pre-caluculation of the factorial
num = 10**7
fact=[0] * num
fact[0]=1
for i in range(1, num):
    fact[i] = (fact[i-1] * i) % mod

def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def f(rr,cc):
    #(0,0)~(r,c)までのコンビネーションの累積和
    #print(rr+cc+2, cc+1)
    #print(combinations_count(rr+cc+2, cc+1))
    #return combinations_count(rr+cc+2, cc+1) - 1
    return (fact[rr+cc+2]%mod * pow(fact[rr+1]*fact[cc+1], mod-2, mod)) % mod -1

ans = f(r2, c2) - f(r2, c1-1) - f(r1-1, c2) + f(r1-1, c1-1)
print(ans % mod)

Fixed submission:
#F
from operator import mul
from functools import reduce

r1, c1, r2, c2 = [int(i) for i in input().split()]
mod = 10**9 + 7

#pre-caluculation of the factorial
num = 10**6*2+3
fact=[0] * num
fact[0]=1
for i in range(1, num):
    fact[i] = (fact[i-1] * i) % mod

def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def f(rr,cc):
    #(0,0)~(r,c)までのコンビネーションの累積和
    #print(rr+cc+2, cc+1)
    #print(combinations_count(rr+cc+2, cc+1))
    #return combinations_count(rr+cc+2, cc+1) - 1
    return (fact[rr+cc+2]%mod * pow(fact[rr+1]*fact[cc+1], mod-2, mod)) % mod -1

ans = f(r2, c2) - f(r2, c1-1) - f(r1-1, c2) + f(r1-1, c1-1)
print(ans % mod)

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

r1, c1, r2, c2 = [int(i) for i in input().split()]
mod = 10**9 + 7

#pre-caluculation of the factorial
num = 10**6
fact=[0] * num
fact[0]=1
for i in range(1, num):
    fact[i] = (fact[i-1] * i) % mod

def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def f(rr,cc):
    #(0,0)~(r,c)までのコンビネーションの累積和
    #print(rr+cc+2, cc+1)
    #print(combinations_count(rr+cc+2, cc+1))
    #return combinations_count(rr+cc+2, cc+1) - 1
    return (fact[rr+cc+2]%mod * pow(fact[rr+1]*fact[cc+1], mod-2, mod)) % mod -1

ans = f(r2, c2) - f(r2, c1-1) - f(r1-1, c2) + f(r1-1, c1-1)
print(ans % mod)

Fixed submission:
#F
from operator import mul
from functools import reduce

r1, c1, r2, c2 = [int(i) for i in input().split()]
mod = 10**9 + 7

#pre-caluculation of the factorial
num = 10**6*2+3
fact=[0] * num
fact[0]=1
for i in range(1, num):
    fact[i] = (fact[i-1] * i) % mod

def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def f(rr,cc):
    #(0,0)~(r,c)までのコンビネーションの累積和
    #print(rr+cc+2, cc+1)
    #print(combinations_count(rr+cc+2, cc+1))
    #return combinations_count(rr+cc+2, cc+1) - 1
    return (fact[rr+cc+2]%mod * pow(fact[rr+1]*fact[cc+1], mod-2, mod)) % mod -1

ans = f(r2, c2) - f(r2, c1-1) - f(r1-1, c2) + f(r1-1, c1-1)
print(ans % mod)

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

r1, c1, r2, c2 = [int(i) for i in input().split()]
mod = 10**9 + 7

def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def f(rr,cc):
    #(0,0)~(r,c)までのコンビネーションの累積和
    #print(rr+cc+2, cc+1)
    #print(combinations_count(rr+cc+2, cc+1))
    return combinations_count(rr+cc+2, cc+1) - 1

ans = f(r2, c2) - f(r2, c1-1) - f(r1-1, c2) + f(r1-1, c1-1)
print(ans % mod)

Fixed submission:
#F
from operator import mul
from functools import reduce

r1, c1, r2, c2 = [int(i) for i in input().split()]
mod = 10**9 + 7

#pre-caluculation of the factorial
num = 10**6*2+3
fact=[0] * num
fact[0]=1
for i in range(1, num):
    fact[i] = (fact[i-1] * i) % mod

def combinations_count(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

def f(rr,cc):
    #(0,0)~(r,c)までのコンビネーションの累積和
    #print(rr+cc+2, cc+1)
    #print(combinations_count(rr+cc+2, cc+1))
    #return combinations_count(rr+cc+2, cc+1) - 1
    return (fact[rr+cc+2]%mod * pow(fact[rr+1]*fact[cc+1], mod-2, mod)) % mod -1

ans = f(r2, c2) - f(r2, c1-1) - f(r1-1, c2) + f(r1-1, c1-1)
print(ans % mod)