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 decimalToBinary(n):  
    return bin(n).replace("0b", "") 
def myXOR(x, y): 
    res = 0 # Initialize result 
  
    # Assuming 32-bit Integer 
    for i in range(31, -1, -1): 
          
        # Find current bits in x and y 
        b1 = x & (1 << i) 
        b2 = y & (1 << i) 
        b1 = min(b1, 1) 
        b2 = min(b2, 1) 
  
        # If both are 1 then 0  
        # else xor is same as OR 
        xoredBit = 0
        if (b1 & b2): 
            xoredBit = 0
        else: 
            xoredBit = (b1 | b2) 
  
        # Update result 
        res <<= 1; 
        res |= xoredBit 
    return res
if __name__ == '__main__':
    n,m,k = map(int,input().split())
    l = []
    count = 0
    for j in range(m):
        l.append(int(input()))
    p = int(input())
    for j in range(m):
        k3 = myXOR(p,l[j])
        k1 = decimalToBinary(k3)
        k2 = list(k1)
        if k2.count('1')<=k:
            count = count+1
    print(count)