Coin Combination Problem

You have 4 bags A, B, C and D each of which includes N coins (there are totally 4N coins). Values of the coins in each bag are a_i, b_i, c_i and d_i respectively.

Find the number of combinations that result when you choose one coin from each bag (totally 4 coins) in such a way that the total value of the coins is V. You should distinguish the coins in a bag.

Constraints

• 1 ≤ N ≤ 1000
• 1 ≤ a_i, b_i, c_i, d_i ≤ 10¹⁶
• 1 ≤ V ≤ 10¹⁶
• All input values are given in integers

Input

The input is given in the following format.

N V
a1 a2 ... aN
b1 b2 ... bN
c1 c2 ... cN
d1 d2 ... dN

Output

Print the number of combinations in a line.

Sample Input 1

3 14
3 1 2
4 8 2
1 2 3
7 3 2

Sample Output 1

9

Sample Input 2

5 4
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

Sample Output 2

625