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 bit(a):
    l=[]
    while a!=1:
        q=int(a/2)
        r=a%2
        l.append(r)
        a=q
    l.append(1)
    l.reverse()
    return l

def samelen(a,b):
    l1=len(a)
    l2=len(b)
    if l1>l2:
        d=l1-l2
        for i in range(0,d):
            b.insert(0,0)
    else:
        d=l2-l1
        for i in range(0,d):
            a.insert(0,0)

def compare(a,b):
    samelen(a,b)
    l1=len(a)
    num=0
    for i in range(0,l1):
        if(a[i]!=b[i]):
            num=num+1
    return num
    
a=input()
n,m,k=list(map(int,a.split()))
b=[]
for i in range(0,m+1):
    c=int(input())
    b.append(c)

c=b[m]
num=0
for i in b:
    e=bit(i)
    if(compare(e,bit(c))<=k):
        
        num=num+1
print(num-1)