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)
def nCr(n, k):
    return int(math.factorial(n)/math.factorial(n-k))

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
    draws = range(n-apb)
    pairs = list(range(n))

    for draw in sorted(draws, reverse=True):
        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 or (A<=a and B<=b and j==apb-1):
                i -= math.factorial(apb - j - 1)
                break

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

    possibles = possibles * math.factorial(n) * nCr(n, n-apb) % 1000000007
    print(possibles)

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: TIME LIMIT EXCEEDED

Test 6

Group: 5

Verdict: TIME LIMIT EXCEEDED