Problem: After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game «Call of Soldiers 3».

The game has (m + 1) players and n types of soldiers in total. Players «Call of Soldiers 3» are numbered form 1 to (m + 1). Types of soldiers are numbered from 0 to n - 1. Each player has an army. Army of the i-th player can be described by non-negative integer xi. Consider binary representation of xi: if the j-th bit of number xi equal to one, then the army of the i-th player has soldiers of the j-th type. 

Fedor is the (m + 1)-th player of the game. He assume that two players can become friends if their armies differ in at most k types of soldiers (in other words, binary representations of the corresponding numbers differ in at most k bits). Help Fedor and count how many players can become his friends.

Input

The first line contains three integers n, m, k (1 ≤ k ≤ n ≤ 20; 1 ≤ m ≤ 1000).

The i-th of the next (m + 1) lines contains a single integer xi (1 ≤ xi ≤ 2n - 1), that describes the i-th player's army. We remind you that Fedor is the (m + 1)-th player.

Output

Print a single integer — the number of Fedor's potential friends.

Examples

Input

7 3 1
8
5
111
17


Output

0


Input

3 3 3
1
2
3
4


Output

3

Solution (in PYTHON):

Solution:

def to_binary_list(integer,n):
        base = '{'+'0'+':'+'0'+str(n)+'b'+'}'
        #print base
        l = list(base.format(integer))
        #print l
        return l

n,m,k = raw_input().split()
n = int(n)
m = int(m)
k = int(k)
l=[]
for i in range(0,m+1):
    army = input()
    l.append(army)


friend = 0
fedor_binary_list = to_binary_list(l[m],n)

for i in range(0,m):
    diffrence = 0
    l1 = to_binary_list(l[i],n)
    for j in range(len(l1)):
        if l1[j] != fedor_binary_list[j]:
            diffrence = diffrence + 1

    #print diffrence
    if diffrence <= k:
        friend = friend + 1

print friend