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 JAVA):

Solution:
var input = readline().split(" "), n = +input[0], m = +input[1], k = +input[2], x = [],
cnt = 0, friends = 0;
for(i = 0; i < m; i++){
	input = +readline();
	x.push(input.toString("2").split("").reverse());
}
input = +readline();
f = input.toString("2").split("").reverse();

for(i = 0; i < m; i++){
	for(j = 0; j < Math.max(x[i].length,f.length); j++){
		if(x[i][j] == undefined){
			x[i][j] = 0;
		}
		if(f[j] == undefined){
			f[j] = 0;
		}
		if((x[i][j] == 1 && f[j] != 1) || (f[j] == 1 && x[i][j] != 1)){
			cnt++;
		}
	}
	if(cnt <= k){
		friends++;
	}
	cnt = 0;
}

print(friends);