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:
# -*- coding: utf-8 -*-

# University Federal of Campina Grande
# Student: Diego Adolfo Silva de Araújo
# Registry: 113210090
# Discipline: Algoritmos Avançados

# Code forces
# Problem: 567B - B. Fedor and New Game
# Time limit per test: 1 second
# Memory limit per test: 256 megabytes
# Input: standard input
# Output: standard output

def compare_weapons(weapon):
    equal_bits = 0
    for j in xrange(n):
        if fedor[j] and weapon & 1 << j == 0:
            equal_bits += 1
        elif not fedor[j] and weapon & 1 << j:
            equal_bits += 1

    return equal_bits

# Types of soldier, number of players and a most K types of soldiers respectively
n, m, k = map(int, raw_input().split())

armies = []
for i in xrange(m):
    army = int(raw_input())
    armies.append(army)

fedor = []
army = int(raw_input())
for i in xrange(n):
    if army & 1 << i:
        fedor.append(True)
    else:
        fedor.append(False)

friends = 0
for i in xrange(m):
    if compare_weapons(armies[i]) <= k:
        friends += 1

print friends