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:
def countSetBits(num):

     # convert given number into binary
     # output will be like bin(11)=0b1101
     binary = bin(num)

     # now separate out all 1's from binary string
     # we need to skip starting two characters
     # of binary string i.e; 0b
     setBits = [ones for ones in binary[2:] if ones=='1']

     return len(setBits)



n,m,k = input().split()
n = int(n)
m = int(m)
k = int(k)

m = m+1
i = 1
p = []
while(i <= m):
    y = int(input())
    p.append(y)
    i = i+1

o = p[::-1]

count = 0
ele = o[0]
#bie = bin(ele)
i = 1
while(i < m):
    r = o[i]
    diff = ele^r
    #de = bin(diff)
    rp = countSetBits(diff)
    if(rp <= k):
        count = count+1

    i = i+1

print(count)