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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Control.Arrow
import Data.List

main :: IO ()
main = getLine >>= main' . map read . words
    where
        main' [n, m] = getLine >> getLine >>= putStrLn . solve n m . map read . words

solve :: Int -> Int -> [Int] -> String
solve n m xs
    | null ys  = "Yes"
    | check m xs = "Yes"
    | otherwise = "No"
    where
        ys = filter ((> 0) . (`mod` n) . length) . group . sort . filter (> 1) $ xs

check :: Int -> [Int] -> Bool
check m xs = ys == 1
    where
        ys = length . group . map length . group . sort $ xs