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:
n, m, k = input().split()
n = int (n)
m = int (m)
k = int (k)
#n = int(input())
#a = list(map(int, input().split()))
#g = list(map(int, input().split()))
#x1, y1, x2, y2 =map(int,input().split())
#n = int(input())
# = [""]*n
#f = [0]*n
#t = [0]*n
#f = []

#h = [""] * n
#f1 = sorted(f, key = lambda tup: tup[0])

#f1 = sorted(t, key = lambda tup: tup[0])
a = [0]*m
for i in range (m):
    a[i] = int(input())
    
f = int(input())
c = 0
for i in range (m):
    cu = f ^ a[i]
    count = 0
    while cu > 0:
        if (cu & 1 == 1): count += 1
        cu >>= 1
    if count <= k:
        #print (i)
        c += 1
print(c)