p03996 CODE FESTIVAL 2016 qual A - LRU Puzzle
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
```python
def reads(offset = 0):
	return [int(i) - offset for i in input().split(' ')]
def Judge(vector):
	length = len(vector)-1
	for i in range(length):
		if(vector[i] > vector[i+1]):		
			return 0
	return 1
(N, M) = reads()
Q = int(input())
A = reads(1)
pos = [-1] * M
pat = []
freq = [0] * (M+1)
freq[0] = N
found = set()
counter = 0
for i in A[::-1]:
	if (i not in found):
		pat.append(i)
		found.add(i)
		pos[i] = counter
		counter += 1
		if(counter == M):
			break
for i in range(M):
	if (pos[i] == -1):
		pat.append(i)	
for i in A[::-1]:
	temp = pos[i]
	if (freq[temp] > 0):
		freq[temp] -= 1
		freq[temp+1] += 1
start = M
for i in range(M):
	if (freq[i] != 0):
		start = i
		break
print("Yes") if Judge(pat[start:]) else print("No")
```