An army of n droids is lined up in one row. Each droid is described by m integers a_1, a_2, ..., a_{m}, where a_{i} is the number of details of the i-th type in this droid's mechanism. R2-D2 wants to destroy the sequence of consecutive droids of maximum length. He has m weapons, the i-th weapon can affect all the droids in the army by destroying one detail of the i-th type (if the droid doesn't have details of this type, nothing happens to it). 

A droid is considered to be destroyed when all of its details are destroyed. R2-D2 can make at most k shots. How many shots from the weapon of what type should R2-D2 make to destroy the sequence of consecutive droids of maximum length?


-----Input-----

The first line contains three integers n, m, k (1 ≤ n ≤ 10^5, 1 ≤ m ≤ 5, 0 ≤ k ≤ 10^9) — the number of droids, the number of detail types and the number of available shots, respectively.

Next n lines follow describing the droids. Each line contains m integers a_1, a_2, ..., a_{m} (0 ≤ a_{i} ≤ 10^8), where a_{i} is the number of details of the i-th type for the respective robot.


-----Output-----

Print m space-separated integers, where the i-th number is the number of shots from the weapon of the i-th type that the robot should make to destroy the subsequence of consecutive droids of the maximum length.

If there are multiple optimal solutions, print any of them. 

It is not necessary to make exactly k shots, the number of shots can be less.


-----Examples-----
Input
5 2 4
4 0
1 2
2 1
0 2
1 3

Output
2 2

Input
3 2 4
1 2
1 3
2 2

Output
1 3



-----Note-----

In the first test the second, third and fourth droids will be destroyed. 

In the second test the first and second droids will be destroyed.

Difficulty: HARD

Solutions:
import sys
from math import *
from bisect import *
from copy import *
MAX = sys.maxsize
MAXN = 10 ** 5 + 10
logT = [0] * MAXN

def arrIN(x=' '):
	return list(map(int, sys.stdin.readline().strip().split(x)))
for i in range(2, MAXN):
	logT[i] = logT[i // 2] + 1

def buildSparse(a):
	n = len(a)
	k = logT[n] + 1
	st = [[-MAX for j in range(k)] for i in range(n)]
	for i in range(n):
		st[i][0] = a[i]
	j = 1
	while 1 << j <= n:
		i = 0
		while i + (1 << j) - 1 < n:
			st[i][j] = max(st[i][j - 1], st[i + (1 << j - 1)][j - 1])
			i += 1
		j += 1
	return st

def query(l, r, st):
	if l > r:
		return -MAX
	tot = r - l + 1
	k = logT[tot]
	return max(st[l][k], st[l + tot - (1 << k)][k])
(n, m, k) = arrIN()
temp = [[0] for _ in range(m)]
for _ in range(n):
	x = arrIN()
	for i in range(m):
		temp[i].append(x[i])
st = []
for i in range(m):
	st.append(buildSparse(temp[i]))
lo = 1
hi = n
t = [0] * m
ans = [0] * m
while lo <= hi:
	mid = (lo + hi) // 2
	i = 1
	f = 0
	while i + mid - 1 <= n:
		for j in range(m):
			t[j] = query(i, i + mid - 1, st[j])
		res = sum(t)
		if res <= k:
			ans = deepcopy(t)
			f = 1
			break
		i += 1
	if f:
		lo = mid + 1
	else:
		hi = mid - 1
print(*ans)


from heapq import heappush, heappop
from sys import setrecursionlimit
from sys import stdin
setrecursionlimit(1000000007)
_data = iter(stdin.read().split('\n'))

def input():
	return next(_data)
(n, m, k) = [int(x) for x in input().split()]
a = tuple((tuple((-int(x) for x in input().split())) for i in range(n)))
heaps1 = tuple(([0] for _ in range(m)))
heaps2 = tuple(([1] for _ in range(m)))
rv = -1
rt = (0,) * m
t = [0] * m
p = 0
for i in range(n):
	ai = a[i]
	for (j, v, heap1) in zip(range(m), ai, heaps1):
		heappush(heap1, v)
		t[j] = heap1[0]
	while -sum(t) > k:
		ap = a[p]
		for (j, v, heap1, heap2) in zip(range(m), ap, heaps1, heaps2):
			heappush(heap2, v)
			while heap1[0] == heap2[0]:
				heappop(heap1)
				heappop(heap2)
			t[j] = heap1[0]
		p += 1
	if rv < i + 1 - p:
		rv = i + 1 - p
		rt = tuple(t)
print(*map(lambda x: -x, rt))


from bisect import bisect_left as bl
from bisect import bisect_right as br
import heapq
import math
from collections import *
from functools import reduce, cmp_to_key
import sys
input = sys.stdin.readline

def li():
	return [int(i) for i in input().rstrip('\n').split()]

def st():
	return input().rstrip('\n')

def val():
	return int(input().rstrip('\n'))

def li2():
	return [i for i in input().rstrip('\n').split(' ')]

def li3():
	return [int(i) for i in input().rstrip('\n')]

def givediff(a, b):
	return sum((max(i, j) for (i, j) in zip(b, a)))
(n, m, k) = li()
l = []
for i in range(n):
	l.append(li())
l1 = [deque() for i in range(m)]
for i in range(m):
	l1[i].append([0, l[0][i]])
(i, j) = (0, 1)
ans = 0
perm = [0] * m if sum(l[0]) > k else l[0][:]
curr = l[0][:]
while j != n:
	for itr in range(m):
		while len(l1[itr]) and l1[itr][-1][-1] <= l[j][itr]:
			l1[itr].pop()
		l1[itr].append([j, l[j][itr]])
	while i < j and givediff(curr, l[j]) > k:
		i += 1
		for itr in range(m):
			while l1[itr][0][0] < i:
				l1[itr].popleft()
			curr[itr] = l1[itr][0][-1]
	for itr in range(m):
		curr[itr] = l1[itr][0][-1]
	if ans < j - i + 1 and givediff(l[j], curr) <= k:
		ans = j - i + 1
		perm = [max(a, b) for (a, b) in zip(l[j], curr)]
	j += 1
print(*perm)


from heapq import heappush, heappop
from sys import setrecursionlimit
from sys import stdin
from collections import defaultdict
setrecursionlimit(1000000007)
_data = iter(stdin.read().split('\n'))

def input():
	return next(_data)
(n, m, k) = [int(x) for x in input().split()]
a = tuple((tuple((-int(x) for x in input().split())) for i in range(n)))
heaps = tuple(([0] for _ in range(m)))
removed = tuple((defaultdict(int) for _ in range(m)))
rv = -1
rt = (0,) * m
t = [0] * m
p = 0
for i in range(n):
	ai = a[i]
	for (j, v, heap) in zip(range(m), ai, heaps):
		heappush(heap, v)
		t[j] = heap[0]
	while -sum(t) > k:
		ap = a[p]
		for (j, v, heap, remd) in zip(range(m), ap, heaps, removed):
			remd[v] += 1
			while heap[0] in remd:
				top = heappop(heap)
				if remd[top] == 1:
					del remd[top]
				else:
					remd[top] -= 1
			t[j] = heap[0]
		p += 1
	if rv < i + 1 - p:
		rv = i + 1 - p
		rt = tuple(t)
print(*map(lambda x: -x, rt))


import math
import random
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
import threading
from collections import defaultdict
threading.stack_size(10 ** 8)
mod = 10 ** 9 + 7
mod1 = 998244353
import os
import sys
from io import BytesIO, IOBase
sys.setrecursionlimit(300000)
BUFSIZE = 8192

class FastIO(IOBase):
	newlines = 0

	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = 'x' in file.mode or 'r' not in file.mode
		self.write = self.buffer.write if self.writable else None

	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines = 0
		return self.buffer.read()

	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b'\n') + (not b)
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines -= 1
		return self.buffer.readline()

	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			(self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode('ascii'))
		self.read = lambda : self.buffer.read().decode('ascii')
		self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

class TreeNode:

	def __init__(self, k, v):
		self.key = k
		self.value = v
		self.left = None
		self.right = None
		self.parent = None
		self.height = 1
		self.num_left = 1
		self.num_total = 1

class AvlTree:

	def __init__(self):
		self._tree = None

	def add(self, k, v):
		if not self._tree:
			self._tree = TreeNode(k, v)
			return
		node = self._add(k, v)
		if node:
			self._rebalance(node)

	def _add(self, k, v):
		node = self._tree
		while node:
			if k < node.key:
				if node.left:
					node = node.left
				else:
					node.left = TreeNode(k, v)
					node.left.parent = node
					return node.left
			elif node.key < k:
				if node.right:
					node = node.right
				else:
					node.right = TreeNode(k, v)
					node.right.parent = node
					return node.right
			else:
				node.value = v
				return

	@staticmethod
	def get_height(x):
		return x.height if x else 0

	@staticmethod
	def get_num_total(x):
		return x.num_total if x else 0

	def _rebalance(self, node):
		n = node
		while n:
			lh = self.get_height(n.left)
			rh = self.get_height(n.right)
			n.height = max(lh, rh) + 1
			balance_factor = lh - rh
			n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
			n.num_left = 1 + self.get_num_total(n.left)
			if balance_factor > 1:
				if self.get_height(n.left.left) < self.get_height(n.left.right):
					self._rotate_left(n.left)
				self._rotate_right(n)
			elif balance_factor < -1:
				if self.get_height(n.right.right) < self.get_height(n.right.left):
					self._rotate_right(n.right)
				self._rotate_left(n)
			else:
				n = n.parent

	def _remove_one(self, node):
		replacement = node.left or node.right
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = replacement
			else:
				node.parent.right = replacement
			replacement.parent = node.parent
			node.parent = None
		else:
			self._tree = replacement
			replacement.parent = None
		node.left = None
		node.right = None
		node.parent = None
		self._rebalance(replacement)

	def _remove_leaf(self, node):
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = None
			else:
				node.parent.right = None
			self._rebalance(node.parent)
		else:
			self._tree = None
		node.parent = None
		node.left = None
		node.right = None

	def remove(self, k):
		node = self._get_node(k)
		if not node:
			return
		if AvlTree._is_leaf(node):
			self._remove_leaf(node)
			return
		if node.left and node.right:
			nxt = AvlTree._get_next(node)
			node.key = nxt.key
			node.value = nxt.value
			if self._is_leaf(nxt):
				self._remove_leaf(nxt)
			else:
				self._remove_one(nxt)
			self._rebalance(node)
		else:
			self._remove_one(node)

	def get(self, k):
		node = self._get_node(k)
		return node.value if node else -1

	def _get_node(self, k):
		if not self._tree:
			return None
		node = self._tree
		while node:
			if k < node.key:
				node = node.left
			elif node.key < k:
				node = node.right
			else:
				return node
		return None

	def get_at(self, pos):
		x = pos + 1
		node = self._tree
		while node:
			if x < node.num_left:
				node = node.left
			elif node.num_left < x:
				x -= node.num_left
				node = node.right
			else:
				return (node.key, node.value)
		raise IndexError('Out of ranges')

	@staticmethod
	def _is_left(node):
		return node.parent.left and node.parent.left == node

	@staticmethod
	def _is_leaf(node):
		return node.left is None and node.right is None

	def _rotate_right(self, node):
		if not node.parent:
			self._tree = node.left
			node.left.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.left
			node.left.parent = node.parent
		else:
			node.parent.right = node.left
			node.left.parent = node.parent
		bk = node.left.right
		node.left.right = node
		node.parent = node.left
		node.left = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	def _rotate_left(self, node):
		if not node.parent:
			self._tree = node.right
			node.right.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.right
			node.right.parent = node.parent
		else:
			node.parent.right = node.right
			node.right.parent = node.parent
		bk = node.right.left
		node.right.left = node
		node.parent = node.right
		node.right = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	@staticmethod
	def _get_next(node):
		if not node.right:
			return node.parent
		n = node.right
		while n.left:
			n = n.left
		return n

class SegmentTree1:

	def __init__(self, data, default, func):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: a + b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class Factorial:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorials = [1, 1]
		self.invModulos = [0, 1]
		self.invFactorial_ = [1, 1]

	def calc(self, n):
		if n <= -1:
			print('Invalid argument to calculate n!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.factorials):
			return self.factorials[n]
		nextArr = [0] * (n + 1 - len(self.factorials))
		initialI = len(self.factorials)
		prev = self.factorials[-1]
		m = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * i % m
		self.factorials += nextArr
		return self.factorials[n]

	def inv(self, n):
		if n <= -1:
			print('Invalid argument to calculate n^(-1)')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		p = self.MOD
		pi = n % p
		if pi < len(self.invModulos):
			return self.invModulos[pi]
		nextArr = [0] * (n + 1 - len(self.invModulos))
		initialI = len(self.invModulos)
		for i in range(initialI, min(p, n + 1)):
			next = -self.invModulos[p % i] * (p // i) % p
			self.invModulos.append(next)
		return self.invModulos[pi]

	def invFactorial(self, n):
		if n <= -1:
			print('Invalid argument to calculate (n^(-1))!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.invFactorial_):
			return self.invFactorial_[n]
		self.inv(n)
		nextArr = [0] * (n + 1 - len(self.invFactorial_))
		initialI = len(self.invFactorial_)
		prev = self.invFactorial_[-1]
		p = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * self.invModulos[i % p] % p
		self.invFactorial_ += nextArr
		return self.invFactorial_[n]

class Combination:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorial = Factorial(MOD)

	def ncr(self, n, k):
		if k < 0 or n < k:
			return 0
		k = min(k, n - k)
		f = self.factorial
		return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD

def powm(a, n, m):
	if a == 1 or n == 0:
		return 1
	if n % 2 == 0:
		s = powm(a, n // 2, m)
		return s * s % m
	else:
		return a * powm(a, n - 1, m) % m

def sort_list(list1, list2):
	zipped_pairs = zip(list2, list1)
	z = [x for (_, x) in sorted(zipped_pairs)]
	return z

def product(l):
	por = 1
	for i in range(len(l)):
		por *= l[i]
	return por

def binarySearchCount(arr, n, key):
	left = 0
	right = n - 1
	count = 0
	while left <= right:
		mid = int((right + left) / 2)
		if arr[mid] < key:
			count = mid + 1
			left = mid + 1
		else:
			right = mid - 1
	return count

def countdig(n):
	c = 0
	while n > 0:
		n //= 10
		c += 1
	return c

def binary(x, length):
	y = bin(x)[2:]
	return y if len(y) >= length else '0' * (length - len(y)) + y

def countGreater(arr, n, k):
	l = 0
	r = n - 1
	leftGreater = n
	while l <= r:
		m = int(l + (r - l) / 2)
		if arr[m] >= k:
			leftGreater = m
			r = m - 1
		else:
			l = m + 1
	return n - leftGreater
(n, m, k) = map(int, input().split())
a = []
ans = []
f = 0
for i in range(n):
	a.append(list(map(int, input().split())))
	su = 0
	for j in range(m):
		su += a[i][j]
	if su <= k:
		f = 1
		ans = a[-1] + []
if f == 0:
	ar = [0] * m
	print(*ar)

def find(x):
	fi = [[] for i in range(m)]
	for i in range(m):
		q = deque([])
		for j in range(x - 1):
			while len(q) > 0 and q[-1][0] <= a[j][i]:
				q.pop()
			q.append((a[j][i], j))
		for j in range(x - 1, n):
			while len(q) > 0 and q[-1][0] <= a[j][i]:
				q.pop()
			q.append((a[j][i], j))
			while q[0][1] <= j - x:
				q.popleft()
			fi[i].append(q[0][0])
	for i in range(len(fi[0])):
		q = []
		su = 0
		for j in range(m):
			su += fi[j][i]
			q.append(fi[j][i])
		if su <= k:
			return q
	return []
st = 1
end = n
while st <= end:
	mid = (st + end) // 2
	f = find(mid)
	if f == []:
		end = mid - 1
	else:
		ans = f
		st = mid + 1
print(*ans)


(n, m, k) = map(int, input().split())
mCnt = 0
ans = [0] * m
start = 0
end = 0
Q = [[] for i in range(m)]
for i in range(n):
	A = list(map(int, input().split()))
	z = 0
	for j in range(m):
		while Q[j] and Q[j][-1][0] < A[j]:
			Q[j].pop()
		Q[j].append([A[j], i])
		z += Q[j][0][0]
	if z <= k:
		end = i + 1
		if mCnt < end - start:
			mCnt = end - start
			for j in range(m):
				ans[j] = Q[j][0][0]
	else:
		while True:
			z = 0
			for j in range(m):
				if Q[j] and Q[j][0][1] == start:
					Q[j].pop(0)
				if Q[j]:
					z += Q[j][0][0]
			start += 1
			if z <= k:
				break
		end += 1
for i in ans:
	print(i, end=' ')


(n, m, k) = map(int, input().split())
q = 0
rez = [0] * int(m)
st = 0
end = 0
p = [[] for i in range(int(m))]
for i in range(int(n)):
	a = list(map(int, input().split()))
	c = 0
	for ii in range(m):
		while p[ii] and p[ii][-1][0] < a[ii]:
			p[ii].pop()
		p[ii].append([a[ii], i])
		c += p[ii][0][0]
	if c <= k:
		end = i + 1
		if q < end - st:
			q = end - st
			for iii in range(m):
				rez[iii] = p[iii][0][0]
	else:
		while 1 == 1:
			c = 0
			for j in range(m):
				if p[j] and p[j][0][1] == st:
					p[j].pop(0)
				if p[j]:
					c += p[j][0][0]
			st += 1
			if c <= k:
				break
		end += 1
for i in rez:
	print(i, end=' ')


from itertools import tee
from sys import setrecursionlimit
from sys import stdin
setrecursionlimit(1000000007)
_data = iter(stdin.read().split('\n'))

def input():
	return next(_data)

class SegTree:

	def __init__(self, n, zero, f):
		while n & n - 1:
			n -= n & -n
		self.n = 2 * n
		self.zero = zero
		self.f = f
		self.t = [self.zero for _ in range(2 * self.n - 1)]

	def __getitem__(self, k):
		return self.t[k + self.n - 1]

	def __setitem__(self, k, v):
		k += self.n - 1
		self.t[k] = v
		while k > 0:
			k = k - 1 >> 1
			self.t[k] = self.f(self.t[2 * k + 1], self.t[2 * k + 2])

	def query(self, a, b):
		ans = self.zero
		t1 = [0]
		t2 = [0]
		t3 = [self.n]
		while t1:
			(k, l, r) = (t1.pop(), t2.pop(), t3.pop())
			if b <= l or r <= a:
				continue
			elif a <= l and r <= b:
				ans = self.f(self.t[k], ans)
			else:
				(t1.append(2 * k + 1), t2.append(l), t3.append(l + r >> 1))
				(t1.append(2 * k + 2), t2.append(l + r >> 1), t3.append(r))
		return ans
(n, m, k) = [int(x) for x in input().split()]
st = tuple((SegTree(n, 0, max) for _ in range(m)))
rv = -1
rt = (0,) * m
p = 0
t = [0] * m
for i in range(n):
	a = tuple((int(x) for x in input().split()))
	for j in range(m):
		st[j][i] = a[j]
		t[j] = max(t[j], a[j])
	while sum(t) > k:
		p += 1
		for j in range(m):
			t[j] = st[j].query(p, i + 1)
	if rv < i + 1 - p:
		rv = i + 1 - p
		rt = tuple(t)
print(*rt)