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 PYTHON):

Solution:
inp = [int(r) for r in raw_input().split()]
n=inp[0]
m=inp[1]
k=inp[2]

count11=0

b=[]
for i in range(0,m+1):
    b.append(int(raw_input().split()[0]))

    
d=list(bin(b[m]))
size=len(d)
for i in range(0,n-size+2):
    d.insert(2,'0')
c11=d[2:len(d)]

for i in range(0,m):
    d11=list(bin(b[i]))[2:len(list(bin(b[i])))]


    for i in range(0,len(c11)-len(d11)):
        d11.insert(0,'0')

    count=0
    
    for j in range(0,len(c11)):
        if int(c11[j])^int(d11[j])==1:
            count=count+1
        
    if count<=k:
        count11=count11+1




print count11