Kortit II

import sys

sys.setrecursionlimit(100000000)
def yli(n, m):
    return kertoma(n)/(kertoma(m)*kertoma(n-m))
kertomat = {}
def kertoma(n):
    if n == 0:
        return 1
    elif n in kertomat:
        return kertomat[n]
    else:
        return kertoma(n-1)*n

an = {}
def a(n, r):
    if r == 1 or n == 3:
        return 1
    if (n, r) in an:
        return an[(n, r)]
    n-=1

    ans = r*a(n, r) + (n+1-r)*a(n, r-1) + n*a(n-1, r-1)
    an[(n, r)] = ans
    return ans


def calculateInputCombinations(input):
    [sticks, awins, bwins] = map(int, input.split(" "))
    draws = sticks - awins - bwins
    if draws<0:
        print(0)
        return
    if (awins==0 or bwins==0) and sticks != draws:
        print(0)
        return
    drawCombinations = yli(sticks, draws)
    n=sticks-draws
    print(int((drawCombinations*kertoma(sticks))%(10**9+7)*a(n, min(awins, bwins))))

n = int(input())
inputs = []
for i in range(n):
    inputs.append(input())
for i in inputs:
    calculateInputCombinations(i)

Test 1

Group: 1, 2, 3, 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 2

Group: 2, 3, 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 3

Group: 3, 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 4

Group: 4, 5

Verdict: TIME LIMIT EXCEEDED

Test 5

Group: 5

Verdict: RUNTIME ERROR

Traceback (most recent call last):
  File "input/code.py", line 46, in <module>
    calculateInputCombinations(i)
  File "input/code.py", line 39, in calculateInputCombinations
    print(int((drawCombinations*kertoma(sticks))%(10**9+7)*a(n, min(awins, bwins))))
OverflowError: int too large to convert to float

Test 6

Group: 5

Verdict: RUNTIME ERROR

Traceback (most recent call last):
  File "input/code.py", line 46, in <module>
    calculateInputCombinations(i)
  File "input/code.py", line 37, in calculateInputCombinations
    drawCombinations = yli(sticks, draws)
  File "input/code.py", line 5, in yli
    return kertoma(n)/(kertoma(m)*kertoma(n-m))
OverflowError: integer division result too large for a float