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:
"""
Codeforces Round #267 (Div. 2)

Problem 467 B. Fedor and New Game

@author yamaton
@date 2015-09-22
"""

import itertools as it
import functools
import operator
import collections
import math
import sys


def solve(xs, n, m, k):
    def diff(a, b):
        return sum(1 for (ca, cb) in zip(a, b) if ca != cb)

    ys = [bin(x)[2:].zfill(n) for x in xs]
    fedor = ys[-1]
    rest = ys[:-1]
    return sum(1 for x in rest if diff(x, fedor) <= k) 


def print_stderr(*args, **kwargs):
    print(*args, file=sys.stderr, **kwargs)


def main():
    [n, m, k] = [int(i) for i in input().strip().split()]
    xs = [int(input().strip()) for _ in range(m+1)]
    result = solve(xs, n, m, k)
    print(result)


if __name__ == '__main__':
    main()