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=[int(x) for x in input().strip().split()]
arr=[]
for i in range(0,m+1):
    arr.append(bin(int(input())))
pivot=arr[-1]
count=0
def differ(a,b):
    a=a[2:]
    b=b[2:]
    c=0
    for i in range(0,min(len(a),len(b))):
        if not a[len(a)-i-1]==b[len(b)-i-1]:
            c+=1
    alpha=a
    if len(alpha)<len(b):
        alpha=b
    temp=alpha[0:max(len(a),len(b))-min(len(a),len(b))]
    for i in temp:
        if i=="1":
            c+=1
    return c
for i in arr[:-1]:
    if differ(pivot,i)<=k:
        count+=1
print(count)