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:
#!/usr/bin/pypy3

from sys import stdin,stderr

def readInts(): return map(int,stdin.readline().strip().split())
def print_err(*args,**kwargs): print(*args,file=stderr,**kwargs)
    
def popcount(v):
    c = 0
    while v>0:
        if v%2==1: c += 1
        v//=2
    return c

def run():
    n,m,k = readInts()
    armies = []
    for _ in range(m):
        army, = readInts()
        armies.append(army)
    fedor, = readInts()
    ok = 0
    for _ in range(m):
        v = fedor ^ armies.pop()
        if popcount(v)<=k: ok += 1
    print(ok)
        
run()