You are given an integer sequence $A_1, A_2, \ldots, A_N$ and an integer $X$. Consider a $N \times N$ matrix $B$, where $B_{i,j} = A_i + A_j$ for each valid $i$ and $j$.
You need to find the number of square submatrices of $B$ such that the sum of their elements is $X$. Formally, find the number of quartets $(x_1, y_1, x_2, y_2)$ such that $1 \le x_1 \le x_2 \le N$, $1 \le y_1 \le y_2 \le N$, $x_2-x_1 = y_2-y_1$ and $\sum_{i=x_1}^{x_2}\sum_{j=y_1}^{y_2} B_{i,j} = X$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $X$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer ― the number of square submatrices with sum $X$.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le X \le 10^6$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^6$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points): the sum of $N$ over all test cases does not exceed $1,000$
Subtask #2 (50 points): original constraints

-----Example Input-----
2
5 36
1 2 3 1 12
4 54
3 3 3 3

-----Example Output-----
6
4

```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 = 'import math\nfor _ in range(int(input())):\n n,x=map(int,input().split())\n a=list(map(int,input().split()))\n count=0\n #y=a.copy()\n #y.sort()\n y=dict()\n for i in range(n):\n  if y.get(a[i]):\n   y[a[i]]+=1\n  else:\n   y[a[i]]=1\n for i in range(n):\n  if a[i]>=x:\n   pass\n  else:\n   p=x-a[i]\n   if y.get(p):\n    count+=y[p]\n   else:\n    pass\n p=math.sqrt(x)\n if n<p:\n  p=n\n b=[]\n k=2\n while k<=p:\n  if x%k==0:\n   b.append(k)\n  k+=1\n #print(b)\n for i in b:\n  summ=0\n  for j in range(i):\n   summ+=a[j]\n  c=[summ]\n  p=0\n  for j in range(i,n):\n   summ+=a[j]\n   summ-=a[p]\n   p+=1\n   c.append(summ)\n  #c.sort()\n  l=len(c)\n  #print(i)\n  #print(c)\n  y=dict()\n  for j in range(l):\n   if y.get(c[j]):\n    y[c[j]]+=1\n   else:\n    y[c[j]]=1\n  for j in range(l):\n   if c[j]>=(x//i):\n    pass\n   else:\n    p=(x//i)-c[j]\n    if y.get(p):\n     count+=y[p]\n    else:\n     pass\n  \n print(count)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14027