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:
# -*- coding: utf-8 -*-
"""
Created on Wed Nov  7 15:41:11 2018

@author: Quaint Sun
"""


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

binary=[]
t=0
while t<m:
    x=int(input())
    if len(str(bin(x))[2:])<n:
        types='0'*(n-len(str(bin(x))[2:]))+str(bin(x))[2:]
    else:
        types=str(bin(x))[2:]
    binary.append(types)
    t=t+1

Fedor=str(bin(int(input())))[2:]
Fedor=['0']*(n-len(Fedor))+list(Fedor)

num=0
for i in binary:
    diff=0
    for j in range(n):
        if Fedor[j]!=i[j]:
            diff=diff+1
    if diff<=k:
        num=num+1
        
print(num)