There are n cities in Westeros. The i-th city is inhabited by a_{i} people. Daenerys and Stannis play the following game: in one single move, a player chooses a certain town and burns it to the ground. Thus all its residents, sadly, die. Stannis starts the game. The game ends when Westeros has exactly k cities left.

The prophecy says that if the total number of surviving residents is even, then Daenerys wins: Stannis gets beheaded, and Daenerys rises on the Iron Throne. If the total number of surviving residents is odd, Stannis wins and everything goes in the completely opposite way.

Lord Petyr Baelish wants to know which candidates to the throne he should support, and therefore he wonders, which one of them has a winning strategy. Answer to this question of Lord Baelish and maybe you will become the next Lord of Harrenholl.


-----Input-----

The first line contains two positive space-separated integers, n and k (1 ≤ k ≤ n ≤ 2·10^5) — the initial number of cities in Westeros and the number of cities at which the game ends. 

The second line contains n space-separated positive integers a_{i} (1 ≤ a_{i} ≤ 10^6), which represent the population of each city in Westeros.


-----Output-----

Print string "Daenerys" (without the quotes), if Daenerys wins and "Stannis" (without the quotes), if Stannis wins.


-----Examples-----
Input
3 1
1 2 1

Output
Stannis

Input
3 1
2 2 1

Output
Daenerys

Input
6 3
5 20 12 7 14 101

Output
Stannis



-----Note-----

In the first sample Stannis will use his move to burn a city with two people and Daenerys will be forced to burn a city with one resident. The only survivor city will have one resident left, that is, the total sum is odd, and thus Stannis wins.

In the second sample, if Stannis burns a city with two people, Daenerys burns the city with one resident, or vice versa. In any case, the last remaining city will be inhabited by two people, that is, the total sum is even, and hence Daenerys wins.

Difficulty: HARD
Tags: Game theory

Starter code:

Solutions:
(n, k) = input().split()
n = int(n)
k = int(k)
s = input()
a = [int(i) for i in s.split()]
nodd = 0
for i in a:
	if i % 2 != 0:
		nodd += 1
neven = len(a) - nodd
if n == k:
	if nodd % 2 == 0:
		print('Daenerys')
	else:
		print('Stannis')
elif nodd <= int((n - k) / 2):
	print('Daenerys')
elif neven <= int((n - k) / 2):
	if k % 2 == 0:
		print('Daenerys')
	else:
		print('Stannis')
elif (n - k) % 2 == 0:
	print('Daenerys')
else:
	print('Stannis')


f = lambda : map(int, input().split())
(n, k) = f()
d = sum((q & 1 for q in f()))
s = n - k >> 1
q = s < d and (k & 1 or s < n - d) if n - k & 1 else k & 1 and s >= n - d
if n == k:
	q = d & 1
print(['Daenerys', 'Stannis'][q])


def f(n, k, l, r):
	if n & 1:
		if k == n:
			return bool(l & 1)
		elif k & 1:
			return n + k <= 2 * l
		else:
			return 2 * l < n + k and 2 * l > n - k - 1
	elif k == n:
		return bool(l & 1)
	elif k & 1:
		return n - k + 1 <= 2 * l
	else:
		return False
(n, k) = list(map(int, input().split(' ')))
a = list(map(int, input().split(' ')))
l = list([i & 1 for i in a]).count(1)
r = n - l
print('Stannis' if f(n, k, l, r) else 'Daenerys')


(n, k) = map(int, input().split())
a = list(map(int, input().split()))
cnt1 = 0
for i in range(n):
	cnt1 += a[i] % 2
ans = ['Daenerys', 'Stannis']
if n == k:
	print(ans[sum(a) % 2])
	exit()
if cnt1 > (n - k) // 2 and n - cnt1 > (n - k) // 2:
	print(ans[(n - k) % 2])
elif cnt1 > (n - k) // 2:
	cnt0 = n - cnt1
	print(ans[(sum(a) - (n - k - cnt0)) % 2])
else:
	print(ans[(sum(a) - cnt1) % 2])


def main():
	(n, k) = map(int, input().split())
	even = 0
	odd = 0
	for elem in input().split():
		if int(elem) % 2 == 0:
			even += 1
		else:
			odd += 1
	turns = n - k
	if turns == 0:
		if odd % 2 == 1:
			return 'Stannis'
		else:
			return 'Daenerys'
	if turns % 2 == 0:
		if k % 2 == 1 and even <= turns // 2:
			return 'Stannis'
		else:
			return 'Daenerys'
	elif k % 2 == 0 and even <= turns // 2 or odd <= turns // 2:
		return 'Daenerys'
	else:
		return 'Stannis'
print(main())


import sys

def solve():
	(n, k) = map(int, input().split())
	a = list(map(int, input().split()))
	odds = sum([x % 2 for x in a])
	evens = n - odds
	if n == k:
		return 'Daenerys' if odds % 2 == 0 else 'Stannis'
	moves = n - k
	if moves % 2 == 0:
		eachmove = moves // 2
		if evens <= eachmove:
			remodds = k
			if remodds % 2 == 1:
				return 'Stannis'
		return 'Daenerys'
	else:
		dmoves = moves // 2
		if odds <= dmoves or (evens <= dmoves and (n - moves) % 2 == 0):
			return 'Daenerys'
		return 'Stannis'
if sys.hexversion == 50594544:
	sys.stdin = open('test.txt')
print(solve())


(n, k) = [int(i) for i in input().split()]
l = [int(i) for i in input().split()]
no = 0
for i in l:
	no += i % 2
ne = n - no
if n == k:
	if no % 2:
		print('Stannis')
	else:
		print('Daenerys')
elif no <= (n - k) // 2:
	print('Daenerys')
elif no % 2:
	if (n - k) % 2 and ne <= (n - k) // 2 and (ne % 2 == 0):
		print('Daenerys')
	elif (n - k) % 2 == 0 and (ne > (n - k) // 2 or ne % 2):
		print('Daenerys')
	else:
		print('Stannis')
elif (n - k) % 2 and ne <= (n - k) // 2 and ne % 2:
	print('Daenerys')
elif (n - k) % 2 == 0 and (ne > (n - k) // 2 or ne % 2 == 0):
	print('Daenerys')
else:
	print('Stannis')


(n, m) = map(int, input().strip().split())
a = list(map(int, input().strip().split()))
x = 0
for i in range(n):
	if a[i] & 1:
		x = x + 1
if n == m:
	if x & 1:
		print('Stannis')
	else:
		print('Daenerys')
elif n - m & 1:
	if m & 1:
		if (n - m) // 2 >= x:
			print('Daenerys')
		else:
			print('Stannis')
	elif (n - m) // 2 >= x or (n - m) // 2 >= n - x:
		print('Daenerys')
	else:
		print('Stannis')
elif m & 1:
	if (n - m) // 2 >= n - x:
		print('Stannis')
	else:
		print('Daenerys')
else:
	print('Daenerys')


(n, k) = map(int, input().split())
o = sum((int(x) & 1 for x in input().split()))
(e, k) = (n - o, n - k)
if not k:
	w = o & 1
elif k & 1:
	if n - k & 1 and o <= k >> 1:
		w = 0
	elif min(o, e) <= k >> 1 and (not n - k & 1):
		w = 0
	else:
		w = 1
elif n - k & 1 and e <= k >> 1:
	w = 1
else:
	w = 0
print(['Daenerys', 'Stannis'][w])


import math, string, itertools, fractions, heapq, collections, re, array, bisect
from itertools import chain, dropwhile, permutations, combinations
from collections import defaultdict, deque

def VI():
	return list(map(int, input().split()))

def main(n, k, a):
	now = sum(a)
	even = sum([x % 2 == 0 for x in a])
	odd = sum([x % 2 == 1 for x in a])
	d = n - k
	D = 'Daenerys'
	S = 'Stannis'
	if n == k:
		ans = [S, D][now % 2 == 0]
	elif d % 2 == 0:
		if k % 2 == 0:
			ans = D
		elif even <= d // 2:
			ans = S
		else:
			ans = D
	elif k % 2 == 0:
		if odd <= d // 2 or even <= d // 2:
			ans = D
		else:
			ans = S
	elif odd <= d // 2:
		ans = D
	else:
		ans = S
	print(ans)

def main_input(info=0):
	(n, k) = VI()
	a = VI()
	main(n, k, a)

def __starting_point():
	main_input()
__starting_point()


R = lambda : list(map(int, input().split()))
(n, k) = R()
a = R()
nch = 0
for i in a:
	if i % 2 == 1:
		nch += 1
ch = n - nch
c = n - k
c_dn = c // 2
c_st = c - c_dn
if c == 0:
	if nch % 2 == 1:
		print('Stannis')
	else:
		print('Daenerys')
elif c_dn >= nch:
	print('Daenerys')
elif c_dn == c_st:
	if ch <= c_st and k % 2 == 1:
		print('Stannis')
	else:
		print('Daenerys')
elif c_dn >= ch and k % 2 == 0:
	print('Daenerys')
else:
	print('Stannis')


import sys
input = []
input_index = 0

def next(type, number=None):

	def next():
		global input, input_index
		while input_index == len(input):
			if sys.stdin:
				input = sys.stdin.readline().split()
				input_index = 0
			else:
				raise Exception()
		input_index += 1
		return input[input_index - 1]
	if number is None:
		result = type(next())
	else:
		result = [type(next()) for _ in range(number)]
	return result
(n, k) = next(int, 2)
bs = next(int, n)
oc = 0
for b in bs:
	oc += 1 if b % 2 == 1 else 0
ec = n - oc
dh = (n - k) // 2
sh = n - k - dh
if n == k:
	if oc % 2 == 0:
		print('Daenerys')
	else:
		print('Stannis')
elif k % 2 == 0:
	if dh == sh:
		print('Daenerys')
	elif dh >= oc or dh >= ec:
		print('Daenerys')
	else:
		print('Stannis')
elif dh == sh:
	if sh >= ec:
		print('Stannis')
	else:
		print('Daenerys')
elif dh >= oc:
	print('Daenerys')
else:
	print('Stannis')


def win(n, k, a):
	count = [0, 0]
	for x in a:
		count[x & 1] += 1
	moves = n - k
	if n == k:
		return count[1] & 1
	if count[1] <= moves // 2:
		return False
	if count[0] <= moves // 2:
		return k & 1
	else:
		return moves & 1
(n, k) = map(int, input().split())
print('Stannis' if win(n, k, map(int, input().split())) else 'Daenerys')


(n, k) = map(int, input().split())
a = list(map(int, input().split()))
cnt = n - k
even = sum([i % 2 == 0 for i in a])
odd = sum([i % 2 == 1 for i in a])
f1 = cnt % 2 == 0 and k % 2 == 1 and (even <= cnt // 2)
f2 = cnt % 2 == 1 and (not (k % 2 == 0 and even <= cnt // 2 or odd <= cnt // 2))
f3 = cnt == 0 and odd % 2 == 1
ans = 'Stannis' if f1 or f2 or f3 else 'Daenerys'
print(ans)