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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "import itertools\nimport bisect\n\nn, A, cf, cm, m = [int(x) for x in input().split()]\nskills = [int(x) for x in input().split()]\nsorted_skills = list(sorted((k, i) for i, k in enumerate(skills)))\nbottom_lift = [0 for i in range(n)]\nfor i in range(1, n):\n    bottom_lift[i] = bottom_lift[i-1] + i * (sorted_skills[i][0] - sorted_skills[i-1][0])\nroot_lift = [0 for i in range(n+1)]\nfor i in range(1, n+1):\n    root_lift[i] = root_lift[i-1] + A - sorted_skills[n-i][0]\n\nmax_level = -1\nfor i in range(n+1):\n    money_left = m - root_lift[i]\n    if money_left < 0: break\n    k = min(bisect.bisect(bottom_lift, money_left), n-i)\n    money_left -= bottom_lift[k-1]\n    min_level = min(A, sorted_skills[k-1][0] + money_left//k) if k > 0 else A\n    level = cf*i + cm*min_level\n    if max_level < level:\n        max_level = level\n        argmax = i\n        argmax_min_level = min_level\n        argmax_k = k\n\nans = [0 for i in range(n)]\nfor i, skill in enumerate(sorted_skills):\n    if i < argmax_k:\n        ans[skill[1]] = argmax_min_level\n    elif i >= n - argmax:\n        ans[skill[1]] = A\n    else:\n        ans[skill[1]] = skill[0]\n\nprint(max_level)\nfor a in ans:\n    print(a, end = ' ')\n    \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14017