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:
n, m, k = map(int, raw_input().split())
xi = []
for i in range(m+1):
    xi.append(input())
c = 0
def dif(s1,s2,k):
    l1 = len(s1)
    l2 = len(s2)
    if l2 < l1:
        s2 = "0"*(l1-l2) + s2
    else:
        s1 = "0"*(l2-l1) + s1
    c = 0
    for i in range(len(s1)):
        if not(s1[i] == s2[i]):
            c+=1
        if c > k:
            return False
    return True
for i in range(m):
    if dif(bin(xi[-1])[2:],bin(xi[i])[2:],k):
        c+=1
print c