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
import math

def main():
    pass

def binary(n):
    return (bin(n).replace("0b", ""))

def decimal(s):
    return (int(s, 2))

def pow2(n):
    p = 0
    while n > 1:
        n //= 2
        p += 1
    return (p)

def isPrime(n):
    if (n == 1):
        return (False)
    else:
        root = int(n ** 0.5)
        root += 1
        for i in range(2, root):
            if (n % i == 0):
                return (False)
        return (True)

def sinp():return sys.stdin.readline().strip()
def iinp():return int(input())
def ninp():return map(int,sys.stdin.readline().strip().split())
def linp():return list(map(int,sys.stdin.readline().strip().split()))

n,m,k=ninp()
l=[]
for i in range(m+1):
    x=iinp()
    s=binary(x)
    s=''.join(reversed(s))
    l.append(s)
l.reverse()
freq=[0]*n
ind=0
cnt=0
ans=0
for c in l[0]:
    if(c=='0'):
        freq[ind]=0
        ind+=1
    elif(c=='1'):
        freq[ind]=1
        ind+=1
l1=len(l[0])
for i in l[1:len(l)+1]:
    l2=len(i)
    for j in range(l1-l2):
        i=i+"0"
    ind=0
    for c in i:
        c1=str(freq[ind])
        if(c!=c1):
            cnt+=1
            ind+=1
        else:
            ind+=1
    if(cnt<=k):
        ans+=1
    cnt=0
print(ans)