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:
n,m,k=[int(x) for x in input().split()]
s=0
a=[]
fe=[]
f=[]
for i in range(m+1):
    a.append(int(input()))
while a[m]>0 :
    fe.append(a[m]%2)
    a[m]=a[m]//2
for i in range(n-len(fe)):
    fe.append(0)
for i in range(m):
    fl=0
    t=0
    f.clear()
    while a[i]>0 :
        f.append(a[i]%2)
        a[i]=a[i]//2
    for i in range(n-len(f)):
        f.append(0) 
    for i in range(n):
        if f[i]!=fe[i]:
            t=t+1
            if t>k:
                fl=1
                break
    if fl!=1:
        s=s+1
print(s)