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:
'''
Name : Jaymeet Mehta
codeforces id :mj_13
Problem : 
'''
from sys import stdin,stdout
def compare(f,s,k):
    xor=f^s
    temp=0
    while(xor!=0):
        temp+=xor&1
        xor>>=1
    return 1 if temp<=k else 0
n,m,k, = map(int,stdin.readline().split()) 
my_lst=[]
for i in range(m):
    my_lst.append(int(stdin.readline()))
fedor=int(stdin.readline())
ans=0
for i in my_lst:
    ans+=compare(fedor,i,k)
print(ans)