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 PYTHON3):

Solution:
"""
n,m,k=map(int,input().split())
ans=-1
data = [0]*(m+1)
for a in range(m+1):
    data[a]=int(input())%n
for a in data:
    if data[m]-k<=a<=data[m]+k:
        ans += 1
print(ans)
"""
"""
n,m,k=map(int,input().split())
ans=0
data=[0]*(m+1)
for a in range(m+1):
    data[a]=format(int(input()),'b').zfill(n)
for a in range(m):
    b = min(len(data[a]),len(data[m]))
    c = bin(data[a]&data[m])
    d = list(c)
    for e in range(b):
        if d[-1-e] == 1:
            f += 1
    if f <=k:
        ans += 1
print(ans)
"""
n,m,k=map(int,input().split())
ans=0
data=[0]*(m+1)
for a in range(m+1):
    data[a]=format(int(input()),'b').zfill(n)
for a in range(m):
    s=list(data[a])
    t=list(data[m])
    anss = 0
    for b in range(n):
        if s[b]!=t[b]:
             anss += 1
    if anss <= k:
        ans += 1
print(ans)