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:
import sys
from collections import *
from heapq import *
import math
import bisect
#def input():
    #return sys.stdin.readline()

n,m,k=map(int,input().split())
fed=''
all=[]
for i in range(m+1):
    if i==m:
        x=int(input())
        fed=bin(x)[2:]
    else:
        x=int(input())
        all.append(bin(x)[2:])
fed=fed[::-1]
cnt=0
for i in all:
    i=i[::-1]
    temp=0
    maxx=max(len(fed),len(i))
    fed+=(maxx-len(fed))*'0'
    i += (maxx - len(i)) * '0'
    for j in range(maxx):
        if i[j]!=fed[j]:
            temp+=1
    if temp<=k:
        cnt+=1
print(cnt)