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:

n, m, k = map(int, raw_input().split()) 

S = [input() for _ in range(m+1)] 

def s_to_array(s): 
    a = [0] * 32 
    i = 0 
    while s: 
        a[i] = (1 if s % 2 ==  1 else 0)
        s /= 2 
        i += 1 

    return a 

def count_diff(a, b): 
    cnt = 0 
    for i in range(len(a)): 
        if a[i] != b[i]: 
            cnt += 1 

    return cnt 

a = s_to_array(S[m]) 
cnt = 0 
for i in range(m): 
    b = s_to_array(S[i]) 
    if count_diff(a, b) <= k: 
        cnt += 1 

print cnt