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:
f = lambda: input()
n,m,k = map(int, f().split())
 
armies = []
bits = []

def bit_diff(a, b):
    diff = 0
    ab = 0
    bb = 0 
    while(a > 0 or b > 0):
        if a > 0:
            ab = a & 1
            a = a >> 1
        else:
            ab = 0

        if b > 0:
            bb = b & 1
            b = b >> 1
        else:
            bb = 0

        if ab != bb:
            diff += 1

    return diff
        
    
for i in range (m+1):
    armies.append(int(f()))

friends = 0
for i in range(0, m):
    if bit_diff(armies[i], armies[m]) <= k:
        friends += 1

print(friends)