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:
def dec2bin(n,t):
    s=''
    while n:
        s=str(n%2)+s
        n/=2
    i=0
    temp=t-len(s)
    while i<temp:
        s='0'+s
        i+=1
    return s
s=raw_input()
a=s.split()
n=int(a[0])
m=int(a[1])
k=int(a[2])
i=0
x=[]
while i<=m:
    temp=int(input())
    temp1=dec2bin(temp,n)
    x.insert(i,temp1)
    i+=1
i=0
count=0
while i<m:
    j=0
    t=0
    while j<n:
        if x[i][j]!=x[m][j]:
            t+=1
        j+=1
    if t<=k:
        count+=1
    i+=1
print count