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:
#COD

def extend(s, n):
    while len(s)<n:
        s = "0" + s
    return s

def diff(s, s1):
    count1 = 0
    for i in range(len(s)):
        if(len(s1) <= i):
            break
        if s[i] != s1[i]:
            count1+=1
    return count1

inp = raw_input(" ")

inp = inp.split(" ")

n = int(inp[0])
m = int(inp[1])
k = int(inp[2])

count = 0

l= []

for i in range(m):
    x = input("")
    if(x<2**n):
        l.append(extend(bin(x)[2:],n))

fed = input("")
fedStr = bin(fed)[2:]
fedStr = extend(fedStr,n)

count = 0

for elem in l:
    if(diff(fedStr[::-1],elem[::-1]) <= k):
        count+=1

print count