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 for i in range(n):\n  if y[i]>=x:\n   break\n  else:\n   p=x-y[i]\n   u=0\n   v=n-1\n   cond=0\n   q=0\n   while u<=v:\n    q=(u+v)//2\n    if y[q]>p:\n     v=q-1\n    elif y[q]<p:\n     u=q+1\n    else:\n     cond=1\n     count+=1\n     break\n   if cond==1:\n    r=q\n    s=q\n    while r>0:\n     if y[r-1]==y[r]:\n      count+=1\n      r-=1\n     else:\n      break\n    while s<n-1:\n     if y[s]==y[s+1]:\n      count+=1\n      s+=1\n     else:\n      break\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 po=0\n pot=0\n for i in b:\n  summ=pot\n  for j in range(po,i):\n   summ+=a[j]\n  po=i\n  pot=summ \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  for t in range(l):\n   if c[t]>=x//i:\n    break\n   else:\n    p=(x//i)-c[t]\n    u=0\n    v=l-1\n    cond=0\n    q=0\n    while u<=v:\n     q=(u+v)//2\n     if c[q]>p:\n      v=q-1\n     elif c[q]<p:\n      u=q+1\n     else:\n      cond=1\n      count+=1\n      break\n    if cond==1:\n     r=q\n     s=q\n     while r>0:\n      if c[r-1]==c[r]:\n       count+=1\n       r-=1\n      else:\n       break\n     while s<l-1:\n      if c[s]==c[s+1]:\n       count+=1\n       s+=1\n      else:\n       break\n    #print(count)\n print(count)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14421