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 = '# cook your dish here\nimport sys\ninput=sys.stdin.readline\nfor _ in range(int(input())):\n n,x=list(map(int,input().split()))\n l=[0]\n pre=[0]*(n+1)\n sum=0\n i=1\n for m in input().split():\n  l.append(int(m))\n  sum+=int(m)\n  pre[i]=sum\n  i+=1\n dict={}\n k=[]\n i=1\n while (i*i)<=x:\n  if x%i==0:\n   k.append(i)\n   if (i*i)!=x:\n    k.append(x//i)\n   else:\n    break\n  i+=1 \n ans=0 \n for a in k:\n  if a>n:\n   continue\n  z=x//a \n  for j in range(a,n+1):\n   s=pre[j]-pre[j-a]\n   if s>z:\n    continue\n   if s in dict:\n    dict[s]+=1\n   else:\n    dict[s]=1\n  for j in range(a,n+1):\n   s=pre[j]-pre[j-a]\n   if s>z:\n    continue\n   if (z-s) in dict:\n    ans+=dict[z-s]\n  for j in range(a,n+1):\n   s=pre[j]-pre[j-a]\n   if s>z:\n    continue\n   dict[s]=0\n   \n print(ans) \n   \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13833