human
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
The above is tricky. Write me a correct solution in PYTHON.
 ... Give me a Python program to print a single integer — the number of Fedor's potential friends?
assistant
#Here is Python program to print a single integer — the number of Fedor's potential friends.

class stack:
    def __init__(self):
        self.ar=[]
    def push(self,d):
        self.ar.append(d)
    def pope(self):
        temp=self.ar.pop()
        return temp

(n,m,k)=map(int,raw_input().split())
s=stack()
for i in range(0,m):
    p=input()
    s.push(p)
num=input()
count=0
for i in range(0,m):
    r=s.pope()
    c=0
    q=num
    for i in range(0,n+1):
        if((q%2)!=(r%2)):
            c=c+1
        q=q/2
        r=r/2
    if(c<=k): count=count+1
print count