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 bin_dist(xx, yy):
    return sum((abs(int(x) - int(y)) for x, y in zip(xx, yy)))


class CodeforcesTask467BSolution:
    def __init__(self):
        self.result = ''
        self.n_m_k = []
        self.armies = []

    def read_input(self):
        self.n_m_k = [int(x) for x in input().split(" ")]
        for _ in range(self.n_m_k[1] + 1):
            self.armies.append(int(input()))

    def process_task(self):
        bins = ["0" * (self.n_m_k[0] - len(bin(x)[2:])) + bin(x)[2:] for x in self.armies]
        self.result = str(sum((1 if bin_dist(bins[-1], x) <= self.n_m_k[2] else 0 for x in bins[:-1])))

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask467BSolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())