CF613B.Skills

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.

莱沙正在玩传奇游戏《Hacknet》最新发布的版本。在此版本中，引入了角色技能机制。现在，每位玩家角色恰好拥有 $n$ 项技能。每项技能由一个非负整数 $a_i$ 表示——即当前技能等级。所有技能具有相同的最高等级 $A$。

除了技能系统外，还新增了所有玩家的全球排名。玩家根据所谓的“战力（Force）”进行排名。一名玩家的战力由以下两部分之和构成：

• 角色已达到完美（即满足 $a_i = A$）的技能数量，乘以系数 $c_f$；
• 所有技能中的最低等级（即 $\min a_i$），乘以系数 $c_m$。

目前，莱沙拥有 $m$ 个 Hacknet 游戏货币单位，他愿意全部用于提升技能。每个货币单位可将任意一项技能的当前等级提升 $1$（前提是该技能当前等级尚未达到 $A$）。请帮助他合理花费这些货币，以使战力值最大化。

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 ≤ 109, 0 ≤ c__f, c__m ≤ 1000, 0 ≤ m ≤ 1015).

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

输入的第一行包含五个以空格分隔的整数 $n$、$A$、$c_f$、$c_m$ 和 $m$（$1 ≤ n ≤ 100\,000$，$1 ≤ A ≤ 10^9$，$0 ≤ c_f,\,c_m ≤ 1000$，$0 ≤ m ≤ 10^{15}$）。

第二行恰好包含 $n$ 个以空格分隔的整数 $a_i$（$0 ≤ a_i ≤ A$）——表示当前各项技能的等级。

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.

第一行输出角色在花费不超过 $m$ 个货币单位的前提下所能达到的最大“力量”（Force）值。

第二行输出 $n$ 个整数 $a'_i$（满足 $a_i \leq a'_i \leq A$），表示为达到上述指定的“力量”值所需达成的各项技能等级，且总花费不超过 $m$ 个货币单位。各数字之间用空格分隔。

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.

在第一个测试用例中，最优策略是将第二项技能提升至其最大值，并将其余两项技能各提升 1。

在第二个测试用例中，应将所有技能均提升至其最大值。