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:

def db(i,j,m):
    
    if len(i) < len(j):
        i = "".join( ["0"]* abs(len(i)-len(j) ) ) + i
    elif len(i) > len(j):
        j = "".join( ["0"]* abs(len(i)-len(j) ) ) + j
    
    dif = 0
    for k in range( min(len(i),len(j))):
        if i[k] != j[k]:
            dif += 1
    
    return dif

def main():
    
    
    n,m,k = [ int(i) for i in raw_input().split(" ") ]
    
    L = []
    for i in range(m+1):
        L.append( "{0:b}".format( int(raw_input()) ) )
    
    total = -1
    for i in L:
        #print i,db(i,L[-1],m)
        if db(i,L[-1],m) <= k:
            total += 1
    
    print total
    
main()