Lesha plays the recently published new version of the legendary game hacknet. In this version character skill mechanism was introduced. Now, each player character has exactly n skills. Each skill is represented by a non-negative integer a_{i} — the current skill level. All skills have the same maximum level A.

Along with the skills, global ranking of all players was added. Players are ranked according to the so-called Force. The Force of a player is the sum of the following values:  The number of skills that a character has perfected (i.e., such that a_{i} = A), multiplied by coefficient c_{f}. The minimum skill level among all skills (min a_{i}), multiplied by coefficient c_{m}. 

Now Lesha has m hacknetian currency units, which he is willing to spend. Each currency unit can increase the current level of any skill by 1 (if it's not equal to A yet). Help him spend his money in order to achieve the maximum possible value of the Force.


-----Input-----

The first line of the input contains five space-separated integers n, A, c_{f}, c_{m} and m (1 ≤ n ≤ 100 000, 1 ≤ A ≤ 10^9, 0 ≤ c_{f}, c_{m} ≤ 1000, 0 ≤ m ≤ 10^15).

The second line contains exactly n integers a_{i} (0 ≤ a_{i} ≤ A), separated by spaces, — the current levels of skills.


-----Output-----

On the first line print the maximum value of the Force that the character can achieve using no more than m currency units.

On the second line print n integers a'_{i} (a_{i} ≤ a'_{i} ≤ A), skill levels which one must achieve in order to reach the specified value of the Force, while using no more than m currency units. Numbers should be separated by spaces.


-----Examples-----
Input
3 5 10 1 5
1 3 1

Output
12
2 5 2 

Input
3 5 10 1 339
1 3 1

Output
35
5 5 5 



-----Note-----

In the first test the optimal strategy is to increase the second skill to its maximum, and increase the two others by 1.

In the second test one should increase all skills to maximum.

Difficulty: HARD
Tags: Sorting

Amortized analysis

Greedy algorithms

Complete search

Dynamic programming
Skill types: Sorting

Amortized analysis

Greedy algorithms

Complete search

Dynamic programming

Starter code:

Solutions:
def main():
	from bisect import bisect
	(n, A, cf, cm, m) = list(map(int, input().split()))
	skills = list(map(int, input().split()))
	xlat = sorted(list(range(n)), key=skills.__getitem__)
	sorted_skills = [skills[_] for _ in xlat]
	(bottom_lift, a, c) = ([], 0, 0)
	for (i, b) in enumerate(sorted_skills):
		c += i * (b - a)
		bottom_lift.append(c)
		a = b
	(root_lift, a) = ([0], 0)
	for b in reversed(sorted_skills):
		a += A - b
		root_lift.append(a)
	max_level = -1
	for (A_width, a) in enumerate(root_lift):
		if m < a:
			break
		money_left = m - a
		floor_width = bisect(bottom_lift, money_left)
		if floor_width > n - A_width:
			floor_width = n - A_width
		money_left -= bottom_lift[floor_width - 1]
		if floor_width > 0:
			floor = sorted_skills[floor_width - 1] + money_left // floor_width
			if floor > A:
				floor = A
		else:
			floor = A
		level = cf * A_width + cm * floor
		if max_level < level:
			(max_level, save) = (level, (A_width, floor, floor_width))
	(A_width, floor, floor_width) = save
	for id in xlat[:floor_width]:
		skills[id] = floor
	for id in xlat[n - A_width:]:
		skills[id] = A
	print(max_level)
	print(' '.join(map(str, skills)))

def __starting_point():
	main()
__starting_point()


(n, A, cf, cm, mN) = map(int, input().split())
a = list(map(int, input().split()))
aCOPY = []
for elem in a:
	aCOPY.append(elem)
a.sort()
aPartialSum = [0]
for elem in a:
	aPartialSum.append(aPartialSum[-1] + elem)
maxScore = 0
ansMAXIBound = 0
ansMAXI = 0
ansMIN = 0
for MAXI in range(n + 1):
	currentScore = cf * MAXI
	if MAXI >= 1:
		mN -= A - a[-MAXI]
	if mN < 0:
		break
	if MAXI == n:
		maxScore = currentScore + A * cm
		ansMAXIBound = 0
		ansMAXI = 10 ** 10
		ansMIN = 0
	l = a[0]
	r = A - 1
	while l < r:
		m = (l + r + 1) // 2
		lA = 0
		rA = n - MAXI - 1
		while lA < rA:
			mA = (lA + rA) // 2
			if a[mA] > m:
				rA = mA - 1
			if a[mA] < m:
				lA = mA + 1
			if a[mA] == m:
				lA = mA
				rA = mA
				break
		lA = min(lA, n - MAXI - 1)
		if a[lA] > m:
			lA -= 1
		expenditure = (lA + 1) * m - aPartialSum[lA + 1]
		if expenditure > mN:
			r = m - 1
		else:
			l = m
	currentScore += l * cm
	if currentScore > maxScore:
		maxScore = currentScore
		ansMAXIBound = a[-MAXI]
		ansMAXI = MAXI
		ansMIN = l
print(maxScore)
inclCount = 0
for i in range(n):
	if aCOPY[i] > ansMAXIBound and inclCount < ansMAXI:
		aCOPY[i] = A
		inclCount += 1
for i in range(n):
	if aCOPY[i] == ansMAXIBound and inclCount < ansMAXI:
		aCOPY[i] = A
		inclCount += 1
	if aCOPY[i] < ansMIN:
		aCOPY[i] = ansMIN
print(' '.join(map(str, aCOPY)))


f = lambda : list(map(int, input().split()))
g = lambda : m - l * p[l - 1] + s[l]
(n, A, x, y, m) = f()
t = sorted(((q, i) for (i, q) in enumerate(f())))
p = [q for (q, i) in t]
s = [0] * (n + 1)
for j in range(n):
	s[j + 1] = p[j] + s[j]
l = r = n
F = L = R = B = -1
while 1:
	if p:
		while l > r or g() < 0:
			l -= 1
		b = min(p[l - 1] + g() // l, A)
	else:
		(b, l) = (A, 0)
	f = x * (n - r) + y * b
	if F < f:
		(F, L, R, B) = (f, l, r, b)
	if not p:
		break
	m += p.pop() - A
	r -= 1
	if m < 0:
		break
print(F)
p = [(i, B if j < L else q if j < R else A) for (j, (q, i)) in enumerate(t)]
for (i, q) in sorted(p):
	print(q)


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=2 ** 51, 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 SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: max(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, A, cf, cm, m) = map(int, input().split())
l = list(map(int, input().split()))
index = [i for i in range(n)]
index = sort_list(index, l)
l.sort()
pre = [0] * (n + 1)
for i in range(1, n + 1):
	pre[i] = pre[i - 1] + l[i - 1]

def find(le, left, x):
	ind = binarySearchCount(l, le, x)
	if ind * x - (pre[ind] - pre[0]) <= left:
		return True
	return False
req = 0
st = 0
end = A
sm = 0
while st <= end:
	mid = (st + end) // 2
	if find(n, m, mid) == True:
		sm = mid
		st = mid + 1
	else:
		end = mid - 1
ans = sm * cm
ind = n
smf = sm
for i in range(n - 1, -1, -1):
	req += A - l[i]
	left = m - req
	if left < 0:
		break
	st = 0
	end = A
	sm = 0
	while st <= end:
		mid = (st + end) // 2
		if find(i, left, mid) == True:
			sm = mid
			st = mid + 1
		else:
			end = mid - 1
	cur = (n - i) * cf + sm * cm
	if cur > ans:
		smf = sm
		ind = i
	ans = max(ans, cur)
for i in range(n - 1, ind - 1, -1):
	l[i] = A
for i in range(ind - 1, -1, -1):
	if l[i] < smf:
		l[i] = smf
l = sort_list(l, index)
print(ans)
print(*l)


import itertools
import bisect
(n, A, cf, cm, m) = [int(x) for x in input().split()]
skills = [int(x) for x in input().split()]
sorted_skills = list(sorted(((k, i) for (i, k) in enumerate(skills))))
bottom_lift = [0 for i in range(n)]
for i in range(1, n):
	bottom_lift[i] = bottom_lift[i - 1] + i * (sorted_skills[i][0] - sorted_skills[i - 1][0])
root_lift = [0 for i in range(n + 1)]
for i in range(1, n + 1):
	root_lift[i] = root_lift[i - 1] + A - sorted_skills[n - i][0]
max_level = -1
for i in range(n + 1):
	money_left = m - root_lift[i]
	if money_left < 0:
		break
	k = min(bisect.bisect(bottom_lift, money_left), n - i)
	money_left -= bottom_lift[k - 1]
	min_level = min(A, sorted_skills[k - 1][0] + money_left // k) if k > 0 else A
	level = cf * i + cm * min_level
	if max_level < level:
		max_level = level
		argmax = i
		argmax_min_level = min_level
		argmax_k = k
ans = [0 for i in range(n)]
for (i, skill) in enumerate(sorted_skills):
	if i < argmax_k:
		ans[skill[1]] = argmax_min_level
	elif i >= n - argmax:
		ans[skill[1]] = A
	else:
		ans[skill[1]] = skill[0]
print(max_level)
for a in ans:
	print(a, end=' ')