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:
# Author : Mradul Tiwari

import heapq as hp
import collections
import bisect
import math
import re


def unpack(func=int):
    return map(func, input().split())


def l_unpack(func=int):
    """list unpack"""
    return list(map(func, input().split()))


def s_unpack(func=int):
    """sorted list unpack"""
    return sorted(map(func, input().split()))


def ml_unpack(n):  # multiple line unpack
    """list of n integers passed on n line, one on each"""
    return [getint() for i in range(n)]


def range_n():
    return range(int(input()))


def counter(a):
    d = {}
    for x in a:
        if x in d:
            d[x] += 1
        else:
            d[x] = 1
    return d


def getint():
    return int(input())


def setbits(x):
    count = 0
    while x:
        x = x & (x - 1)
        count += 1
    return count


def main():
    n, m, k = unpack()
    a = ml_unpack(m + 1)
    me = a[-1]
    count = 0
    for i in range(m):
        if setbits(me ^ a[i]) <= k:
            count += 1
    print(count)


main()