Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = list(map(int, input().split()))
mx = max(a)

def ncr(n, r, p):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den, p - 2, p)) % p
p=10**9+7

ans = 0
comb = 0
for i in a:
    if mx == i:
        continue
    tmp = ncr(mx, i, p)
    if comb <= tmp:
        ans = i 
        comb = tmp
print(mx, ans, sep=" ")

Fixed submission:
import bisect
n = int(input())
a = list(map(int, input().split()))
a = sorted(a)
m = max(a)
half_idx = bisect.bisect_left(a, m//2)

def ncr(n, r, p):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den, p - 2, p)) % p
p=10**9+7 

if n == 2:
    print(a[1], a[0])
    exit()

if 1 <= half_idx < n-1:
    if min(a[half_idx-1], m-(a[half_idx-1])) >= max(min(a[half_idx], m-(a[half_idx])), min(a[half_idx+1], m-(a[half_idx+1]))):
        print(m, a[half_idx-1])
    elif min(a[half_idx], m-(a[half_idx])) >= max(min(a[half_idx-1], m-(a[half_idx-1])), min(a[half_idx+1], m-(a[half_idx+1]))):
        print(m, a[half_idx])
    elif min(a[half_idx+1], m-(a[half_idx+1])) >= max(min(a[half_idx], m-(a[half_idx])), min(a[half_idx-1], m-(a[half_idx-1]))):
        print(m, a[half_idx+1])
elif half_idx == 0:
    if min(a[half_idx], m-(a[half_idx])) >= min(a[half_idx+1], m-(a[half_idx+1])):
        print(m, a[half_idx])
    elif min(a[half_idx+1], m-(a[half_idx+1])) >= min(a[half_idx], m-(a[half_idx])):
        print(m, a[half_idx+1])
elif half_idx == n-1:
    if min(a[half_idx], m-(a[half_idx])) >= min(a[half_idx-1], m-(a[half_idx-1])):
        print(m, a[half_idx])
    elif min(a[half_idx-1], m-(a[half_idx-1])) >= min(a[half_idx], m-(a[half_idx])):
        print(m, a[half_idx-1])

Buggy python submission (verdict: Time Limit Exceeded):
import bisect
n = int(input())
a = list(map(int, input().split()))
a = sorted(a)
m = max(a)
half_idx = bisect.bisect_left(a, m//2)

def ncr(n, r, p):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den, p - 2, p)) % p
p=10**9+7 

if n == 2:
    print(a[1], a[0])
    exit()

if 1 <= half_idx < n-1:
    if ncr(m, a[half_idx-1], p) >= max(ncr(m, a[half_idx], p), ncr(m, a[half_idx+1], p)):
        print(m, a[half_idx-1])
    elif ncr(m, a[half_idx], p) >= max(ncr(m, a[half_idx-1], p), ncr(m, a[half_idx+1], p)):
        print(m, a[half_idx])
    elif ncr(m, a[half_idx+1], p) >= max(ncr(m, a[half_idx], p), ncr(m, a[half_idx-1], p)):
        print(m, a[half_idx+1])
elif half_idx == 0:
    if ncr(m, a[half_idx], p) >= ncr(m, a[half_idx+1], p):
        print(m, a[half_idx])
    elif ncr(m, a[half_idx+1], p) >= ncr(m, a[half_idx], p):
        print(m, a[half_idx+1])
elif half_idx == n-1:
    if ncr(m, a[half_idx], p) >= ncr(m, a[half_idx-1], p):
        print(m, a[half_idx])
    elif ncr(m, a[half_idx-1], p) >= ncr(m, a[half_idx], p):
        print(m, a[half_idx-1])

Fixed submission:
import bisect
n = int(input())
a = list(map(int, input().split()))
a = sorted(a)
m = max(a)
half_idx = bisect.bisect_left(a, m//2)

def ncr(n, r, p):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den, p - 2, p)) % p
p=10**9+7 

if n == 2:
    print(a[1], a[0])
    exit()

if 1 <= half_idx < n-1:
    if min(a[half_idx-1], m-(a[half_idx-1])) >= max(min(a[half_idx], m-(a[half_idx])), min(a[half_idx+1], m-(a[half_idx+1]))):
        print(m, a[half_idx-1])
    elif min(a[half_idx], m-(a[half_idx])) >= max(min(a[half_idx-1], m-(a[half_idx-1])), min(a[half_idx+1], m-(a[half_idx+1]))):
        print(m, a[half_idx])
    elif min(a[half_idx+1], m-(a[half_idx+1])) >= max(min(a[half_idx], m-(a[half_idx])), min(a[half_idx-1], m-(a[half_idx-1]))):
        print(m, a[half_idx+1])
elif half_idx == 0:
    if min(a[half_idx], m-(a[half_idx])) >= min(a[half_idx+1], m-(a[half_idx+1])):
        print(m, a[half_idx])
    elif min(a[half_idx+1], m-(a[half_idx+1])) >= min(a[half_idx], m-(a[half_idx])):
        print(m, a[half_idx+1])
elif half_idx == n-1:
    if min(a[half_idx], m-(a[half_idx])) >= min(a[half_idx-1], m-(a[half_idx-1])):
        print(m, a[half_idx])
    elif min(a[half_idx-1], m-(a[half_idx-1])) >= min(a[half_idx], m-(a[half_idx])):
        print(m, a[half_idx-1])