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`.

Examples

Input

2 2
3
2 1 2


Output

Yes


Input

3 2
3
2 1 2


Output

No


Input

2 3
3
3 2 1


Output

Yes


Input

3 3
6
1 2 2 3 3 3


Output

No
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

N,M = map(int,input().split())
Q = int(input())
A = [int(x) for x in input().split()]

used = [False] * (M+1)
arr = []
for x in A[::-1]:
    if used[x]:
        continue
    used[x] = True
    arr.append(x)
for x in range(1,M+1):
    if used[x]:
        continue
    arr.append(x)

x_to_i = {x:i for i,x in enumerate(arr,1)}

made = [N] + [0] * M

for x in A[::-1]:
    i = x_to_i[x]
    if made[i-1] > 0:
        made[i-1] -= 1
        made[i] += 1

L = 0
prev = M+100
for x in arr[::-1]:
    if x >= prev:
        break
    prev = x
    L += 1

x = sum(made[::-1][:L+1])
answer = 'Yes' if x == N else 'No'
print(answer)