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:
from sys import stdin, stdout
import math
import random
import time


def sumSquare(a):
    s = 0
    for i in range(len(a)):
        s += a[i]*a[i]
    return s


def C():
    n = int(input())
    a = list(map(int, stdin.readline().split()))
    while True:
        for i in range(n):
            op = False
            for j in range(i+1, n):
                if (a[i] | a[j]) > max(a[i], a[j]):
                    op = True
                    if a[i] > a[j]:
                        temp_ai = a[i]
                        temp_aj = a[j]
                        a[i] = temp_ai | temp_aj
                        a[j] = temp_ai & temp_aj

                    else:
                        temp_ai = a[i]
                        temp_aj = a[j]
                        a[i] = temp_ai & temp_aj
                        a[j] = temp_ai | temp_aj

        if not op:
            break

    print(sumSquare(a))


def num_of_set_bits(n):
    count = 0
    while n>0:
        n = n & n-1
        count += 1
    return count


def main():
    # t = list(map(int, stdin.readline().split()))
    n, m, k = list(map(int, stdin.readline().split()))
    x = [int(input()) for i in range(m+1)]
    fedor = x[-1]
    friends = 0
    for i in range(len(x)-1):
        diff = fedor ^ x[i]
        if num_of_set_bits(diff) <= k:
            friends += 1
    print(friends)


if __name__ == '__main__':
    main()