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:
'''Fedor and New Game Solution
'''

def parsebin(num, N):
    bn = ''
    for expn in range(N - 1, -1, -1):
        # print(expn)
        if 2**expn > num:
            bn += '0'
        else:
            num -= 2**expn
            bn += '1'

    return(bn)        


'''routine
'''
N, M, K = list(map(int, input().split()))
players = []
for player in range(M + 1):
    players.append(parsebin(int(input()), N))

fedor = players.pop()
friends = 0
for player in players:
    notmatch = 0
    for pos in range(N):
        if fedor[pos] != player[pos]:
            notmatch += 1
        if notmatch > K:
            break
    if notmatch <= K:
        friends += 1

print(friends)