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:
#import time
n,m,k=raw_input().split()
n=int(n)
m=int(m)
k=int(k)
#s=time.time()
def to_binary(x):
    help=[524288,262144,131072,65536,32768,16384,8192,4096,2048,1024,512,256,128,64,32,16,8,4,2,1]
    d=[]
    for i in help:
        q,r=divmod(x,i)
        d.append(str(q))
        x=r
    delimiter=''
    return delimiter.join(d)

binary=[]
for i in range(0,m+1):
    q=int(raw_input())
    binary.append(to_binary(q))

  
fedor=binary[m]
frnd=0
for player in binary:
    cnt=0
    for j in range(19,-1,-1):
        if cnt>k:
            break
        elif fedor[j]!=player[j]:
            cnt=cnt+1
        elif j==0:
            frnd=frnd+1

print frnd-1