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:
import math

def binary(num):
    bi = ""
    while(num!=0):
        rem = num%2
        bi += str(rem)
        num = num/2
    bi = bi[::-1]
    length = len(bi)
    pi = ""
    for _ in xrange(32-len(bi)):
        pi += "0"
    bi = pi + bi
    return bi
    
[n,m,k] = map(int, raw_input().split())
a = []
for i in xrange(0,m):
    a.append(binary(int(input())))
fedor = binary(int(input()))

max_c = 0
for binary in a:
    count = 0
    for i in xrange(32):
        if(binary[i]!=fedor[i]):
            count+=1
    if(count<=k):
        max_c+=1
print max_c