Kortit II

import copy
from itertools import combinations
import math

def ith_permutation(l, i):
    n=len(l)
    fact = [1] * n
    perm = [0] * n

    for k in range(1, n):
        fact[k] = fact[k - 1] * k

    for k in range(n):
        perm[k] = i // fact[n - 1 - k]
        i = i % fact[n - 1 - k]

    for k in range(n - 1, 0, -1):
        for j in range(k - 1, -1, -1):
            if perm[j] <= perm[k]:
                perm[k] += 1

    return map(lambda x: l[x], perm)

t=int(input())

vals = []
for test in range(t):
    vals.append(map(int, input().split()))

for test in range(t):
    n, a, b = vals[test]
    if a + b == 1 or a + b > n:
        print(0)
        continue
    possibles = 0
    apb = a + b
    _fac = math.factorial(apb) - 1
    for draws in combinations(range(n), n - a - b):
        pairs = list(range(n))

        for draw in draws[::-1]:
            pairs.pop(draw)
        i = _fac
        while i >= 0:
            perm = ith_permutation(pairs, i)
            A = B = 0
            for j, (pair1, pair2) in enumerate(zip(pairs, perm)):
                if pair2 < pair1:
                    A += 1
                elif pair2 > pair1:
                    B += 1

                if A > a or B > b:
                    i -= math.factorial(apb - j) - 1
                    break

            if A == a and B == b:
                possibles += 1

            i -= 1
    possibles = possibles * math.factorial(n) % 1000000007
    print(possibles)

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: TIME LIMIT EXCEEDED

Test 6

Group: 5

Verdict: TIME LIMIT EXCEEDED