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:
def to_bin(a,n):
    if a==0:
        return '0'*n
    s=""
    while int(a)!=0:
        if(a%2==0) : s+='0'
        else: s+='1'
        a/=2
    while len(s)<n:
        s='0'+s
    return s

def solve(x,y,n):
    count=0
    for i in range(n):
        if x[i]!=y[i] : count+=1
    return count


n,m,k=map(int,input().split())

a=[]
for i in range(m+1):
    a.append(int(input()))

curr=a[m]

ans=0
for i in range(m):
    if (bin(curr^a[i]).count('1')<=k):
        #print (to_bin(curr,n))
        #print(to_bin(a[i],n))
        ans+=1
print(ans)