In this problem you are given a sequence of $N$ positive integers $S[1],S[2],\dots,S[N]$. In addition you are given an integer $T$, and your aim  is to find the number of quadruples $(i,j,k,l)$, such that $1 \le i < j < k < l \le N$, and $S[i] + S[j] + S[k] + S[l] = T$.  That is, the number of ways of picking four numbers from the sequence summing up to $T$.

-----Constraints:-----
For all test cases,
- $1 \le N \le 5000$
- $1 \le T \le 10^6$
- $1 \le S[i] \le 10^9$, for all $i$.
Subtask $1:10\%$
It is guaranteed that $N \le 50$.
Subtask $2:50\%$
It is guaranteed that $N \le 300$.
Subtask $3:40\%$
No additional guarantees.

-----Input Format:-----
There is only one line of input with $N+2$ space separated integers. The first two integers are $N$ and $T$. The next $N$ integers are $S[1],S[2],\dots,S[N]$.

-----Output Format:-----
A single integer which is the number of valid quadruples.

-----Sample Input 1:-----
6 20 3 1 1 2 5 10

-----Sample Output 1:-----
1

-----Explanation 1:-----
The quadruple $(1,4,5,6)$ is valid  because $S[1]+S[4]+S[5]+S[6]=3+2+5+10=20$. You can check that no other quadruple is valid and hence the answer is $1$.

-----Sample Input 2:-----
6 13 1 2 3 4 5 4 

-----Sample Output 2:-----
3

-----Explanation 2:-----
You can verify that the only quadruples that are valid are $(2,3,4,6),(1,3,4,5)$  and $(1,3,5,6)$. Thus, the answer is $3$.

-----Note:-----
As the answer might be large, please use 64 bit integers (long long int in
C/C++ and long in Java) instead of 32 bit int.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\nfrom operator import itemgetter\ninp=list(map(int, input().split()))\nn, t = inp[0], inp[1]\narray=inp[2:]\nsomme=[]\nfor i in range(n-1):\n    for j in range(i+1,n):\n        somme.append((array[i]+array[j], {i, j}))\nsomme.sort(key=itemgetter(0))\ni_end=len(somme)-1\ncounter=0\nfor i in range(len(somme)-1):\n    while i_end>i and somme[i][0]+somme[i_end][0]>t:\n        i_end-=1\n    if i_end==i:\n        break\n    appo=i_end\n    while appo>i and somme[i][0]+somme[appo][0]==t:\n        if len(somme[i][1]&somme[appo][1])==0:\n            counter+=1\n        appo-=1\nprint(counter//3)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13665