Problem:
Score: 300 points

Problem Statement

Takahashi has decided to hold fastest-finger-fast quiz games. Kizahashi, who is in charge of making the scoreboard, is struggling to write the program that manages the players' scores in a game, which proceeds as follows.

A game is played by N players, numbered 1 to N. At the beginning of a game, each player has K points.

When a player correctly answers a question, each of the other N-1 players receives minus one (-1) point. There is no other factor that affects the players' scores.

At the end of a game, the players with 0 points or lower are eliminated, and the remaining players survive.

In the last game, the players gave a total of Q correct answers, the i-th of which was given by Player A_i.
For Kizahashi, write a program that determines whether each of the N players survived this game.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq K \leq 10^9

1 \leq Q \leq 10^5

1 \leq A_i \leq N\ (1 \leq i \leq Q)

Input

Input is given from Standard Input in the following format:

N K Q
A_1
A_2
.
.
.
A_Q

Output

Print N lines. The i-th line should contain Yes if Player i survived the game, and No otherwise.

Sample Input 1

6 3 4
3
1
3
2

Sample Output 1

No
No
Yes
No
No
No

In the beginning, the players' scores are (3, 3, 3, 3, 3, 3).

Player 3 correctly answers a question. The players' scores are now (2, 2, 3, 2, 2, 2).

Player 1 correctly answers a question. The players' scores are now (2, 1, 2, 1, 1, 1).

Player 3 correctly answers a question. The players' scores are now (1, 0, 2, 0, 0, 0).

Player 2 correctly answers a question. The players' scores are now (0, 0, 1, -1, -1, -1).

Players 1, 2, 4, 5 and 6, who have 0 points or lower, are eliminated, and Player 3 survives this game.

Sample Input 2

6 5 4
3
1
3
2

Sample Output 2

Yes
Yes
Yes
Yes
Yes
Yes

Sample Input 3

10 13 15
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9

Sample Output 3

No
No
No
No
Yes
No
No
No
Yes
No

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

module ABC141

  ! <module>s to import
  use, intrinsic :: iso_fortran_env

  ! require all variables to be explicitly declared
  implicit none

  ! accessibility of <subroutine>s and <function>s in this <module>
  public :: task_C

  ! contained <subroutine>s and <function>s are below
  contains

  subroutine task_C

    ! variables for this <subroutine>
    integer(INT32) :: id_player_answered
    integer(INT32) :: num_players
    integer(INT32) :: val_points_init
    integer(INT32) :: num_questions

    ! arrays for this <subroutine>
    integer(INT32), dimension(:), allocatable :: list_player_points

    ! support variables for this <subroutine>
    integer(INT32) :: itr_p
    integer(INT32) :: itr_q

    ! STEP.01
    ! read out the given data
    read(unit=INPUT_UNIT, fmt=*) num_players, val_points_init, num_questions

    ! STEP.02
    ! allocate the array to store the given data
    allocate( list_player_points  (1:num_players)   )

    ! STEP.03
    ! initialize the list of points
    list_player_points(:) = 0_INT32

    ! STEP.04
    ! read out the given data
    ! update the points of the players
    do itr_q = 1_INT32, num_questions, 1_INT32
      read(unit=INPUT_UNIT, fmt=*) id_player_answered
      list_player_points( id_player_answered ) = list_player_points( id_player_answered ) + 1_INT32
    end do

    ! STEP.05
    ! output the answer of this task
    ! update the points of the players
    do itr_p = 1_INT32, num_players, 1_INT32

      if (list_player_points(itr_p) .gt. num_questions - val_points_init) then
        write(unit=OUTPUT_UNIT, fmt='(A)', advance='yes') 'Yes'
      else
        write(unit=OUTPUT_UNIT, fmt='(A)', advance='yes') 'No'
      end if

    end do

    ! STEP.06
    ! deallocate the array to store the given data
    deallocate( list_player_points )

    ! STEP.END
    return

  end subroutine task_C

end module ABC141


program main

  ! <module>s to import
  use, non_intrinsic :: ABC141

  ! require all variables to be explicitly declared
  implicit none

  call task_C

end program main