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 dec_to_bin(q, n):
    ans = ''
    while q > 0 or len(ans) < n:
        ans += str(q % 2)
        q //= 2
        if q == 0 and len(ans) < n:
            ans += '0'
    return ans[::-1]


n, m, k = map(int, input().split())
a = []
for i in range(m):
    a.append(dec_to_bin(int(input()), n))
f = dec_to_bin(int(input()), n)
cnt = 0
for j in range(m):
    dif = abs(len(f) - len(a[j]))
    if dif > k:
        continue
    if len(f) <= len(a[j]):
        for _ in range(len(f)):
            if f[_] != a[j][_]:
                dif += 1
                if dif > k:
                    dif = 0
                    break
            if _ == len(f) - 1:
                cnt += 1
    else:
        for _ in range(len(a[j])):
            if a[j][_] != f[_]:
                dif += 1
                if dif > k:
                    break
            if _ == len(a[j]) - 1:
                cnt += 1
print(cnt)