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 ai, bi, ci and di 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 ≤ ai, bi, ci, di ≤ 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.

Examples

Input

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


Output

9


Input

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


Output

625

Solution (in CPP):

Solution:
#define _CRT_SECURE_NO_WARNINGS
#include "bits/stdc++.h"

#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fr(x) freopen(x,"r",stdin)
#define fw(x) freopen(x,"w",stdout)
#define iout(x) printf("%d\n",x)
#define lout(x) printf("%lld\n",x)
#define REP(x,l,u) for(ll x = l;x<u;x++)
#define RREP(x,l,u) for(ll x = l;x>=u;x--)
#define complete_unique(a) a.erase(unique(a.begin(),a.end()),a.end())
#define mst(x,a) memset(x,a,sizeof(x))
#define all(a) a.begin(),a.end()
#define PII pair<int,int>
#define PLL pair<ll,ll>
#define MP make_pair
#define sqr(x) ((x)*(x))
#define lowbit(x) ((x)&(-(x)))
#define lson (ind<<1)
#define rson (ind<<1|1)
#define se second
#define fi first
#define sz(x) ((int)x.size())
#define EX0 exit(0);

typedef  long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ld;
using namespace std;
typedef vector<ll> VLL;
typedef vector<int> VI;
const int block_size = 320;
typedef complex<ll> point;
const ll mod = 1e9 + 7;
const ll inf = 1e9 + 7;
const ld eps = 1e-9;
const db PI = atan(1) * 4;

template<typename T, typename S>inline bool upmin(T&a, const S&b) { return a > b ? a = b, 1 : 0; }
template<typename T, typename S>inline bool upmax(T&a, const S&b) { return a < b ? a = b, 1 : 0; }

ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a%b); }
namespace SOLVE {
	
	void main() {
		ll n, v;
		cin >> n >> v;
		map<ll, ll> freq;
		vector<VLL> og(4, VLL(n));

		REP(i, 0, 4) {
			REP(j, 0, n) {
				cin >> og[i][j];
			}
		}
		REP(i, 0, n) {
			REP(j, 0, n) {
				freq[og[0][i] + og[1][j]]++;
			}
		}
		ll ans = 0;
		REP(i, 0, n) {
			REP(j, 0, n) {
				ans += freq[v - og[2][i] - og[3][j]];
			}
		}

		cout << ans << endl;
	}
}


signed main() {

	int t;
	//    in(t);
	t = 1;
	while (t--) {
		SOLVE::main();

	}

	return 0;
}