jsumabat has ~n~ integers, and has a definition of what he calls k-Intersecting Numbers.

He considers a pair of integers "k-Intersecting" if the binary representation of the numbers ~x~ and ~y~ differs from each other in exactly ~k~ bits.

For example, if ~k = 2~, the pairs of integers ~x = 5~ and ~y =3~ is k-intersecting because the binary representation ~x=101~ and ~y=011~ differs exactly in two bits.

Now here's the problem: jsumabat wants to know how many pairs of integers ~(i, j)~ are in his sequence so that ~i < j~ and the pair of integers ~a_i~ and ~a_j~ is k-intersecting.

Can you help jsumabat find the number of pairs that fit in these constraints?

Input Specifications

The first line contains two integers ~n~ and ~k~ ~(2 \le n \le 10^5, 0 \le k \le 14)~ - the number of integers jsumabat has and the number of bits in which integers in a k-intersecting pair should differ.

The second line contains the sequence ~a_1, a_2, \dots, a_n~ ~(0 \le a_i \le 10^4)~, which jsumabat has.

Output Specifications

Print the number of pairs ~(i, j)~ so that ~i < j~ and the pair of integers ~a_i~ and ~a_j~ is k-intersecting.

Sample Input 1

4 1
0 3 2 1

Sample Output 1

4

Sample Input 2

6 0
200 100 100 100 200 200

Sample Output 2

6

Sample Explanation

In the first sample, there are 4 k-intersecting pairs:

• ~(1, 3)~,
• ~(1, 4)~,
• ~(2, 3)~,
• ~(2, 4)~.

In the second sample where ~k=0~, there are 6 k-intersecting pairs:

• ~(1, 5)~,
• ~(1, 6)~,
• ~(2, 3)~,
• ~(2, 4)~,
• ~(3, 4)~,
• ~(5, 6)~.