Problem:
Score : 1200 points

Problem Statement

There are N arrays.
The length of each array is M and initially each array contains integers (1，2，...，M) in this order.

Mr. Takahashi has decided to perform Q operations on those N arrays.
For the i-th (1≤i≤Q) time, he performs the following operation.

Choose an arbitrary array from the N arrays and move the integer a_i (1≤a_i≤M) to the front of that array. For example, after performing the operation on a_i=2 and the array (5，4，3，2，1), this array becomes (2，5，4，3，1).

Mr. Takahashi wants to make N arrays exactly the same after performing the Q operations.
Determine if it is possible or not.

Constraints

2≤N≤10^5

2≤M≤10^5

1≤Q≤10^5

1≤a_i≤M

Input

The input is given from Standard Input in the following format:

N M
Q
a_1 a_2 ... a_Q

Output

Print Yes if it is possible to make N arrays exactly the same after performing the Q operations.
Otherwise, print No.

Sample Input 1

2 2
3
2 1 2

Sample Output 1

Yes

You can perform the operations as follows.

Sample Input 2

3 2
3
2 1 2

Sample Output 2

No

Sample Input 3

2 3
3
3 2 1

Sample Output 3

Yes

You can perform the operations as follows.

Sample Input 4

3 3
6
1 2 2 3 3 3

Sample Output 4

No

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

program lru_puzzle
  implicit none
  integer :: n, m, q, a(100000) = 0, i, k
  integer :: x = 0, p(100000) = 0, r(100000) = 0, c(0:100000) = 0
  logical :: u(100000) = .false.
  read(*,*) n, m
  read(*,*) q
  read(*,*) a(1:q)
  do i = q, 1, -1
    if (u(a(i))) cycle
    x = x+1
    p(x) = a(i)
    u(a(i)) = .true.
  end do
  do i = 1, m
    if (u(i)) cycle
    x = x+1
    p(x) = i
  end do
  do i = 1, m
    r(p(i)) = i
  end do
  c(0) = n
  do i = q, 1, -1
    k = r(a(i))
    if (c(k-1) > 0) then
      c(k-1) = c(k-1)-1
      c(k) = c(k)+1
    end if
  end do
  k = 0
  do while (c(k) == 0)
    k = k+1
  end do
  do i = k+1, m-1
    if (p(i) > p(i+1)) then
      write(*,'(a)') "No"
      stop
    end if
  end do
  write(*,'(a)') "Yes"
end program lru_puzzle