Kortit II

from collections import deque
from math import factorial
import sys

t = sys.stdin.readline()


for line in sys.stdin:
    n, a, b = [int(x) for x in line.split()]
    if a + b > n: 
        print('{}'.format(0))
        continue
    elif (a == 0 and b != 0) or (b == 0 and a != 0):
        print('{}'.format(0))
        continue

    ties = n - a - b

    tot_cards2 = [x for x in range(1, n-ties+1)]
    valid_games = 0

    tot_runs = 0

    pos_ties = int(factorial(n)/factorial(n-ties))

    def search(c1, cards2, p1, p2):

        if c1 == 0:
            if p1 == a and p2 == b:
                global valid_games
                valid_games += 1
            
        else:
            for i in range(len(cards2)):
                
                cs2 = cards2[:]
                if len(cards2) == 0:
                    break

                if cs2[i] == c1:
                    continue
                else:
                    c2 = cs2.pop(i)
                    if c1 > c2:
                        search(c1-1, cs2, p1+1, p2)
                    elif c1 < c2:
                        search(c1-1, cs2, p1, p2+1)

    if a == 0 and b == 0:
        print('{}'.format(pos_ties))
        continue

    if a == 1 or b == 1:
        valid_games = 1
    else:
        search(n-ties, tot_cards2, 0, 0)

    total_amount = (valid_games*factorial((n-ties)))*(factorial(n)/factorial(n-ties))**2
    print('{}'.format(int(total_amount % ((10**9)+7))))

Test 1

Group: 1, 2, 3, 4, 5

Verdict: WRONG ANSWER

Test 2

Group: 2, 3, 4, 5

Verdict: WRONG ANSWER

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 "/box/input/code.py", line 24, in <module>
    pos_ties = int(factorial(n)/factorial(n-ties))
OverflowError: integer division result too large for a float

Test 6

Group: 5

Verdict: RUNTIME ERROR

Traceback (most recent call last):
  File "/box/input/code.py", line 24, in <module>
    pos_ties = int(factorial(n)/factorial(n-ties))
OverflowError: integer division result too large for a float