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 PYTHON):

Solution:
import sys

# def main() :
#         nRooms = int(sys.stdin.readline())
#         res = 0
#         for i in range(nRooms) :
#                 p, q = map(int, sys.stdin.readline().split())
#                 if p < q - 1 :
#                         res +=1
#         print(res)

# main()


# print(bin(7).count("1"))


def main() :
        n, m, k = map(int, sys.stdin.readline().split())
        N = 2**n
        nMax = bin(N-1).count("1")
        army = [0 for _ in range(m)]
        res = 0
        for i in range(m) :
                army[i] = int(sys.stdin.readline())
        armyFriend = int(sys.stdin.readline())

        for i in range(m) :
                s = ((2*N - 1 - army[i]) ^ armyFriend)
                # print(nMax)
                if bin(s).count("1") >= nMax + 1 - k :
                        res += 1

        print(res)

main()