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 Fri Apr  3 15:16:34 2020

@author: SOUVIK PAN
"""
def solve( A,  B): 
   
    count = 0 
  
    # since, the numbers are less than 2^31 
    # run the loop from '0' to '31' only 
    for i in range(0,32): 
  
        # right shift both the numbers by 'i' and 
        # check if the bit at the 0th position is different 
        if ((( A >>  i) & 1) != (( B >>  i) & 1)):  
             count=count+1
           
    return count
n,m,k = map(int,input().split())
a=[]
for i in range(m):
    a.append(int(input()))
b= int(input())
sm=0
for i in range(m):
    if solve(a[i],b) <=k:
        sm+=1
    
    #print(solve(a[i],b))
print(sm)