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
from sys import stdin
from itertools import repeat
def main():
    n, m = map(int, stdin.readline().split())
    q = int(stdin.readline())
    a = map(int, stdin.readline().split(), repeat(10, q))
    a = [x - 1 for x in a]
    l = [[] for i in xrange(m)]
    la = []
    for i in xrange(q - 1, -1, -1):
        x = a[i]
        if not l[x]:
            la.append(x)
        l[x].append(i)
    ok = 1
    b = [q] * n
    f = [0] * m
    xt = 0
    for i, x in enumerate(la):
        j = 0
        for y in l[x]:
            if j < n and y < b[j]:
                b[j] = y
                j += 1
        if j < n:
            ok = 0
            b[j] = -1
        if not ok:
            while f[xt]:
                  xt += 1
            if x != xt:
                print "No"
                return
            f[xt] = 1
        else:
            f[x] = 1
    print "Yes"
main()