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.

The first line of the input contains five space-separated integers n, A, c_f, c_m and m (1≤n≤100000, 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.

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.