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:
a = map(int,raw_input().split())
b = a[1]
d = []
x = 0
y = 0
counter = 0
totalcounter =0
while b>=0:
     z = ""
     c = int(raw_input())
     e = "{0:b}".format(c)
     f = len(e)
     while f<a[0]:
         z = z + "0"
         f +=1 
     z = z + str(e)
     d.append(z)
     b -=1
while y<len(d)-1:
    x = 0
    counter = 0
    while x<a[0]:
        if d[y][x] != d[len(d)-1][x]:
            counter +=1
        x +=1
    if counter <= a[2]:   
        totalcounter +=1
    y+=1
    
print totalcounter