This problem is interactive.

You should guess hidden number x which is between 1 and M = 10004205361450474, inclusive.

You could use up to 5 queries.

In each query, you can output an increasing sequence of k ≤ x integers, each between 1 and M, inclusive, and you will obtain one of the following as an answer:

  * either the hidden number belongs to your query sequence, in this case you immediately win; 
  * or you will be given where the hidden number is located with respect to your query sequence, that is, either it is less than all numbers from the sequence, greater than all numbers from the sequence, or you will be given such an i that the hidden number x is between the i-th and the (i+1)-st numbers of your sequence. 



See the interaction section for clarity.

Be aware that the interactor is adaptive, i.e. the hidden number can depend on queries the solution makes. However, it is guaranteed that for any solution the interactor works non-distinguishable from the situation when the hidden number is fixed beforehand.

Hacks are allowed only with fixed hidden number. A hack is represented by a single integer between 1 and M. In all pretests the hidden number is fixed as well.

Interaction

You can make up to 5 queries. To make a query print a number k (1 ≤ k ≤ 10^4) and then an increasing sequence t_0 < t_1 < … < t_{k-1} of k numbers, each between 1 and M, inclusive. If k > x, you lose.

You get one integer as a response. 

  * If it is -2, it means you made an invalid query or you lost. Exit immediately after receiving -2 and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream. 
  * If it is -1, you guessed the number and should terminate too. 
  * Otherwise you get a number i between 0 and k, inclusive, denoting where the hidden number is, with respect to the printed numbers. If i = 0, then x < t_0. If i = k, then t_{k-1} < x. Otherwise t_{i-1} < x < t_i. 



After printing a query do not forget to output end of line and flush the output. Otherwise you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.

Example

Input

 
2

0

-1

Output

2 2 3

2 20 30

3 5 7 9

Note

In the first example the number 5 is hidden.

Difficulty: VERY_HARD
Tags: Dynamic programming
Skill types: Dynamic programming

Starter code:

Solutions:
from sys import stdin, stdout
max_k = 10000
max_shift = [max_k]
for t in range(1, 5):
	max_shift.append(max_shift[t - 1] * (max_k + 1) + max_k)

def get_right(left, t):
	if left >= max_k:
		return left + max_shift[t - 1] - 1
	k = left
	if k > max_k:
		k = max_k
	if t == 1:
		return left + k - 1
	new_left = left
	for i in range(k):
		new_left = get_right(new_left, t - 1) + 2
	return get_right(new_left, t - 1)
left = 1
right = 10004205361450474
k = 1
for t in range(5, 0, -1):
	if t == 1:
		right = get_right(left, 1)
		request = range(left, right + 1)
	else:
		request = []
		request_item = left - 1
		for i in range(k):
			request_item = get_right(request_item + 1, t - 1) + 1
			request.append(request_item)
	print(len(request), ' '.join([str(x) for x in request]))
	stdout.flush()
	reply = int(stdin.readline())
	if reply in (-1, -2):
		exit()
	if reply > 0:
		left = request[reply - 1] + 1
	k = left
	if k > max_k:
		k = max_k


import math
import sys
MAX = 10004205361450474
QMAX = 10000
LOCAL = False

def inp():
	return sys.stdin.readline().rstrip()
ANS = -1
ROUNDS = 0
if LOCAL:
	ANS = int(inp())
	assert ANS <= MAX

def do_query(values):
	global ROUNDS
	if LOCAL:
		print('QUERY {}...{} (len={})'.format(values[0], values[-1], len(values)))
		ROUNDS += 1
		if max(values) > MAX:
			print('Value too large: {}'.format(max(values)))
			resp = -2
		try:
			i = values.index(ANS)
			print('CORRECT! ROUNDS={}'.format(ROUNDS))
			resp = -1
		except ValueError:
			if ROUNDS == 5:
				print('NOT SOLVED IN 5 ROUNDS.')
				resp = -2
			else:
				resp = len(values)
				for (i, v) in enumerate(values):
					if ANS < v:
						resp = i
						break
		print('  => {}'.format(resp))
	else:
		print(len(values), *values, flush=True)
		resp = int(inp())
	if resp < 0:
		sys.exit()
	return resp

def trim_query(query):
	if max(query) <= MAX:
		return query
	res = [q for q in query if q <= MAX]
	if max(query) != MAX:
		res.append(MAX)
	return res
CACHE = [{}, {1: 5, 7: 2045, 2047: 20468426, 20468428: 120488427, 120488429: 220508428, 220508430: 320528429, 320528431: 420548430, 420548432: 520568431, 520568433: 620588432, 620588434: 720608433, 720608435: 820628434, 820628436: 920648435, 920648437: 1020668436, 1020668438: 1120688437, 1120688439: 1220708438, 1220708440: 1320728439, 1320728441: 1420748440, 1420748442: 1520768441, 1520768443: 1620788442, 1620788444: 1720808443, 1720808445: 1820828444, 1820828446: 1920848445, 1920848447: 2020868446, 2020868448: 2120888447, 2120888449: 2220908448, 2220908450: 2320928449, 2320928451: 2420948450, 2420948452: 2520968451, 2520968453: 2620988452, 2620988454: 2721008453, 2721008455: 2821028454, 2821028456: 2921048455, 2921048457: 3021068456, 3021068458: 3121088457, 3121088459: 3221108458, 3221108460: 3321128459, 3321128461: 3421148460, 3421148462: 3521168461, 3521168463: 3621188462, 3621188464: 3721208463, 3721208465: 3821228464, 3821228466: 3921248465, 3921248467: 4021268466, 4021268468: 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8222108510: 8322128509, 8322128511: 8422148510, 8422148512: 8522168511, 8522168513: 8622188512, 8622188514: 8722208513, 8722208515: 8822228514, 8822228516: 8922248515, 8922248517: 9022268516, 9022268518: 9122288517, 9122288519: 9222308518, 9222308520: 9322328519, 9322328521: 9422348520, 9422348522: 9522368521, 9522368523: 9622388522, 9622388524: 9722408523, 9722408525: 9822428524, 9822428526: 9922448525, 9922448527: 10022468526, 10022468528: 10122488527, 10122488529: 10222508528, 10222508530: 10322528529, 10322528531: 10422548530, 10422548532: 10522568531, 10522568533: 10622588532, 10622588534: 10722608533, 10722608535: 10822628534, 10822628536: 10922648535, 10922648537: 11022668536, 11022668538: 11122688537, 11122688539: 11222708538, 11222708540: 11322728539, 11322728541: 11422748540, 11422748542: 11522768541, 11522768543: 11622788542, 11622788544: 11722808543, 11722808545: 11822828544, 11822828546: 11922848545, 11922848547: 12022868546, 12022868548: 12122888547, 12122888549: 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16023668588: 16123688587, 16123688589: 16223708588, 16223708590: 16323728589, 16323728591: 16423748590, 16423748592: 16523768591, 16523768593: 16623788592, 16623788594: 16723808593, 16723808595: 16823828594, 16823828596: 16923848595, 16923848597: 17023868596, 17023868598: 17123888597, 17123888599: 17223908598, 17223908600: 17323928599, 17323928601: 17423948600, 17423948602: 17523968601, 17523968603: 17623988602, 17623988604: 17724008603, 17724008605: 17824028604, 17824028606: 17924048605, 17924048607: 18024068606, 18024068608: 18124088607, 18124088609: 18224108608, 18224108610: 18324128609, 18324128611: 18424148610, 18424148612: 18524168611, 18524168613: 18624188612, 18624188614: 18724208613, 18724208615: 18824228614, 18824228616: 18924248615, 18924248617: 19024268616, 19024268618: 19124288617, 19124288619: 19224308618, 19224308620: 19324328619, 19324328621: 19424348620, 19424348622: 19524368621, 19524368623: 19624388622, 19624388624: 19724408623, 19724408625: 19824428624, 19824428626: 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23725208665: 23825228664, 23825228666: 23925248665, 23925248667: 24025268666, 24025268668: 24125288667, 24125288669: 24225308668, 24225308670: 24325328669, 24325328671: 24425348670, 24425348672: 24525368671, 24525368673: 24625388672, 24625388674: 24725408673, 24725408675: 24825428674, 24825428676: 24925448675, 24925448677: 25025468676, 25025468678: 25125488677, 25125488679: 25225508678, 25225508680: 25325528679, 25325528681: 25425548680, 25425548682: 25525568681, 25525568683: 25625588682, 25625588684: 25725608683, 25725608685: 25825628684, 25825628686: 25925648685, 25925648687: 26025668686, 26025668688: 26125688687, 26125688689: 26225708688, 26225708690: 26325728689, 26325728691: 26425748690, 26425748692: 26525768691, 26525768693: 26625788692, 26625788694: 26725808693, 26725808695: 26825828694, 26825828696: 26925848695, 26925848697: 27025868696, 27025868698: 27125888697, 27125888699: 27225908698, 27225908700: 27325928699, 27325928701: 27425948700, 27425948702: 27525968701, 27525968703: 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31426748742: 31526768741, 31526768743: 31626788742, 31626788744: 31726808743, 31726808745: 31826828744, 31826828746: 31926848745, 31926848747: 32026868746, 32026868748: 32126888747, 32126888749: 32226908748, 32226908750: 32326928749, 32326928751: 32426948750, 32426948752: 32526968751, 32526968753: 32626988752, 32626988754: 32727008753, 32727008755: 32827028754, 32827028756: 32927048755, 32927048757: 33027068756, 33027068758: 33127088757, 33127088759: 33227108758, 33227108760: 33327128759, 33327128761: 33427148760, 33427148762: 33527168761, 33527168763: 33627188762, 33627188764: 33727208763, 33727208765: 33827228764, 33827228766: 33927248765, 33927248767: 34027268766, 34027268768: 34127288767, 34127288769: 34227308768, 34227308770: 34327328769, 34327328771: 34427348770, 34427348772: 34527368771, 34527368773: 34627388772, 34627388774: 34727408773, 34727408775: 34827428774, 34827428776: 34927448775, 34927448777: 35027468776, 35027468778: 35127488777, 35127488779: 35227508778, 35227508780: 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39128288819: 39228308818, 39228308820: 39328328819, 39328328821: 39428348820, 39428348822: 39528368821, 39528368823: 39628388822, 39628388824: 39728408823, 39728408825: 39828428824, 39828428826: 39928448825, 39928448827: 40028468826, 40028468828: 40128488827, 40128488829: 40228508828, 40228508830: 40328528829, 40328528831: 40428548830, 40428548832: 40528568831, 40528568833: 40628588832, 40628588834: 40728608833, 40728608835: 40828628834, 40828628836: 40928648835, 40928648837: 41028668836, 41028668838: 41128688837, 41128688839: 41228708838, 41228708840: 41328728839, 41328728841: 41428748840, 41428748842: 41528768841, 41528768843: 41628788842, 41628788844: 41728808843, 41728808845: 41828828844, 41828828846: 41928848845, 41928848847: 42028868846, 42028868848: 42128888847, 42128888849: 42228908848, 42228908850: 42328928849, 42328928851: 42428948850, 42428948852: 42528968851, 42528968853: 42628988852, 42628988854: 42729008853, 42729008855: 42829028854, 42829028856: 42929048855, 42929048857: 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185857630286: 185957650285, 185957650287: 186057670286, 186057670288: 186157690287, 186157690289: 186257710288, 186257710290: 186357730289, 186357730291: 186457750290, 186457750292: 186557770291, 186557770293: 186657790292, 186657790294: 186757810293, 186757810295: 186857830294, 186857830296: 186957850295, 186957850297: 187057870296, 187057870298: 187157890297, 187157890299: 187257910298, 187257910300: 187357930299, 187357930301: 187457950300, 187457950302: 187557970301, 187557970303: 187657990302, 187657990304: 187758010303, 187758010305: 187858030304, 187858030306: 187958050305, 187958050307: 188058070306, 188058070308: 188158090307, 188158090309: 188258110308, 188258110310: 188358130309, 188358130311: 188458150310, 188458150312: 188558170311, 188558170313: 188658190312, 188658190314: 188758210313, 188758210315: 188858230314, 188858230316: 188958250315, 188958250317: 189058270316, 189058270318: 189158290317, 189158290319: 189258310318, 189258310320: 189358330319, 189358330321: 189458350320, 189458350322: 189558370321, 189558370323: 189658390322, 189658390324: 189758410323, 189758410325: 189858430324, 189858430326: 189958450325, 189958450327: 190058470326, 190058470328: 190158490327, 190158490329: 190258510328, 190258510330: 190358530329, 190358530331: 190458550330, 190458550332: 190558570331, 190558570333: 190658590332, 190658590334: 190758610333, 190758610335: 190858630334, 190858630336: 190958650335, 190958650337: 191058670336, 191058670338: 191158690337, 191158690339: 191258710338, 191258710340: 191358730339, 191358730341: 191458750340, 191458750342: 191558770341, 191558770343: 191658790342, 191658790344: 191758810343, 191758810345: 191858830344, 191858830346: 191958850345, 191958850347: 192058870346, 192058870348: 192158890347, 192158890349: 192258910348, 192258910350: 192358930349, 192358930351: 192458950350, 192458950352: 192558970351, 192558970353: 192658990352, 192658990354: 192759010353, 192759010355: 192859030354, 192859030356: 192959050355, 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def plan_round(low, rounds_left, need_query):
	cache = CACHE[rounds_left - 1]
	if rounds_left >= 2 and (not need_query) and (low in cache):
		return (None, cache[low])
	if low >= QMAX:
		if rounds_left == 1:
			result = (list(range(low, low + QMAX)), low + QMAX - 1)
		else:
			(_, left_max) = plan_round(low, rounds_left - 1, False)
			width = left_max - low + 1
			query = [low + width]
			for _ in range(QMAX - 1):
				query.append(query[-1] + 1 + width)
			right_max = query[-1] + width
			result = (query, right_max)
	elif rounds_left == 1:
		result = (list(range(low, low + low)), low + low - 1)
	else:
		(_, left_max) = plan_round(low, rounds_left - 1, False)
		query = [left_max + 1]
		for _ in range(low - 1):
			(_, mid_max) = plan_round(query[-1] + 1, rounds_left - 1, False)
			query.append(mid_max + 1)
		(_, right_max) = plan_round(query[-1] + 1, rounds_left - 1, False)
		result = (query, right_max)
	if rounds_left >= 2:
		cache[low] = result[1]
	return result

def do_round(low, rounds_left):
	(query, high) = plan_round(low, rounds_left, True)
	query = trim_query(query)
	pos = do_query(query)
	if pos == 0:
		do_round(low, rounds_left - 1)
	else:
		do_round(query[pos - 1] + 1, rounds_left - 1)

def main():
	do_round(1, 5)
main()


from math import *
from sys import stdout
import os

def get_5th():
	return 1

def full_5th(k):
	return min(10000, k)

def get_4th():
	now = 1
	now = now + get_5th()
	now = now + full_5th(now + 1)
	return now

def full_4th(k):
	if k >= 10000:
		return 10000 * (10000 + 1) + 10000
	now_seg = full_5th(k)
	ret = k
	seg_point = k - 1
	for i in range(k + 1):
		ret = ret + now_seg
		seg_point = seg_point + now_seg + 1
		now_seg = full_5th(seg_point + 1)
	return ret

def get_3rd():
	now = 1
	now = now + get_4th()
	now = now + full_4th(now + 1)
	return now

def full_3rd(k):
	if k >= 10000:
		return full_4th(k) * (10000 + 1) + 10000
	now_seg = full_4th(k)
	ret = k
	seg_point = k - 1
	for i in range(k + 1):
		ret = ret + now_seg
		seg_point = seg_point + now_seg + 1
		now_seg = full_4th(seg_point + 1)
	return ret

def get_2nd():
	now = 1
	now = now + get_3rd()
	now = now + full_3rd(now + 1)
	return now

def full_2nd(k):
	if k >= 10000:
		return full_3rd(k) * (10000 + 1) + 10000
	now_seg = full_3rd(k)
	ret = k
	seg_point = k - 1
	for i in range(k + 1):
		ret = ret + now_seg
		seg_point = seg_point + now_seg + 1
		now_seg = full_3rd(seg_point + 1)
	return ret

def get_1st():
	now = 1
	now = now + get_2nd()
	now = now + full_2nd(now + 1)
	return now

def get_list(l, full, one):
	if l == 1:
		return [1 + one()]
	point_num = min(l, 10000)
	ret = []
	now_seg = full(l)
	seg_point = l - 1
	for i in range(point_num):
		seg_point = seg_point + now_seg + 1
		ret.append(seg_point)
		now_seg = full(seg_point + 1)
	return ret

def output(lis):
	n = len(lis)
	out = '%d ' % n
	for (idx, x) in enumerate(lis):
		out = out + '%d ' % x
	test = None
	if test == None:
		print('%s\n' % out)
		stdout.flush()
		pt = int(input())
	else:
		pt = n
		for (idx, x) in enumerate(lis):
			if test == x:
				pt = -1
				break
			if test < x:
				pt = idx
				break
		if pt == -1:
			(l, r) = (-1, -1)
		elif pt == n:
			(l, r) = (lis[n - 1], -1)
		elif pt == 0:
			(l, r) = (-1, lis[0])
		else:
			(l, r) = (lis[pt - 1], lis[pt])
		print(pt, l, r)
	if pt != -1:
		return 1 if pt == 0 else lis[pt - 1] + 1
	return pt

def check(l, now):
	temp = output(now)
	if temp == -1:
		os._exit(0)
	ret = max(l, temp)
	return ret
(l, r) = (1, 10004205361450474)
now = get_list(l, full_2nd, get_2nd)
l = check(l, now)
now = get_list(l, full_3rd, get_3rd)
l = check(l, now)
now = get_list(l, full_4th, get_4th)
l = check(l, now)
now = get_list(l, full_5th, get_5th)
l = check(l, now)
output([x + l for x in range(min(l, 10000))])