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

def read():
    return int(input())

def reads(sep=None):
    return list(map(int, input().split()))

def f(m, a):
	sa = set(a)
	seen = set()
	r = []
	for n in a[::-1]:
		if n not in seen:
			r.append(n)
			seen.add(n)
	for i in range(m):
		if (i+1) not in sa:
			r.append(i+1)
	return r

def isSorted(a):
	for i in range(1, len(a)):
		if a[i-1] > a[i]:
			return False
	return True

n, m = reads()
q = read()
a = reads()

r = f(m, a)
count = [0] * (m+1)
count[0] = n

table = [-1] * (m+1)
for i in range(len(r)):
	table[r[i]] = i

for aa in a[::-1]:
	index = table[aa]
	if 0 < count[index]:
		count[index] -= 1
		count[index+1] += 1

to = m
for i in range(m):
	if 0 < count[i]:
		to = i
		break

if isSorted(r[to:]):
	print('Yes')
else:
	print('No')
