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:
import sys, math, itertools, random, bisect
from collections import defaultdict
# sys.setrecursionlimit(999999999)
INF = 10**18
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def input(): return sys.stdin.readline().strip()
mod = 10**9 + 7

# MAX = 100001

# def sieve():
# 	isPrime = [True]*(MAX)
# 	isPrime[0] = False
# 	isPrime[1] = False

# 	for i in range(2,MAX):
# 		if isPrime[i]:
# 			for j in range(i*i, MAX, i):
# 				isPrime[j] = False
    
# 	primes = [2]
# 	for i in range(3,MAX,2):
# 		if isPrime[i]: primes.append(i)
# 	return primes
    
test = 1
# test = int(input())
for _ in range(test):
    n,m,k = get_ints()
    a = []
    for i in range(m+1):
        a.append(int(input()))
    
    last = [0]*20
    for i in range(20):
        if a[-1]&1<<i:
            last[i] = 1
    
    ans = 0
    for i in range(m):
        x = [0]*20
        for j in range(20):
            if a[i]&1<<j:
                x[j] = 1
        diff = 0

        for j in range(20):
            if x[j]!=last[j]: diff += 1
        
        if diff<=k: ans += 1
    print(ans)