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:
from sys import stdin

def diff( a, b ):
        return sum( a[i] != b[i] for i in range( len(a) ) )

getBin = lambda x, n: x >= 0 and str( bin(x) )[2:].zfill( n ) or "-" + str( bin(x) )[3:].zfill(n)

n, m, k = map( int, stdin.readline().split() )
x = []

for i in xrange( m ):
        x.append( int( stdin.readline() ) )

fedor = str( getBin( int( stdin.readline() ), 22 ) )

y = [ str( getBin(a, 22) ) for a in x ]

cnt = 0
for w in y:
        if ( diff( w, fedor ) <= k ):
                cnt += 1

print cnt