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 = 'def binary_search(b,item,n):\n lb = 0\n a = b[:]\n ub = n-1\n cnt = 1\n f = 0\n while lb<=ub:\n  mid = (lb+ub)//2\n  if a[mid] == item:\n   f = 1\n   a.pop(mid)\n   ub = ub - 1\n   cnt = cnt + 1\n  elif a[mid] > item:\n   ub = mid - 1\n  else:\n   lb = mid + 1\n\n if f == 1:\n  return cnt\n else:\n  return False\n\n\ncases = int(input())\nfor v in range(cases):\n a = list(map(int,input().strip().split()))\n n = a[0]\n x = a[1]\n a = list(map(int,input().strip().split()))\n \n cnt = 0\n\n for i in range(1,n+1):\n  if x%i == 0:\n   side = i\n   freq = 0\n   subsetsum = []\n   left = 0\n   right = i-1\n   s = sum(a[:right+1])\n   if s > x:\n    freq = freq + 1\n   else:\n    subsetsum.append(s)\n   while right < n - 1:\n    right += 1\n    s = s + a[right] - a[left]\n    left += 1\n    \n    if s > x:\n     freq = freq + 1\n    else:\n     subsetsum.append(s)\n    \n   y = x//side\n   subsetsum.sort()\n   \n   for r in range(n-side+1-freq):\n    h = binary_search(subsetsum,y-subsetsum[r],n-side+1-freq)\n    if h:\n     cnt = cnt + h-1\n    \n\n\n print(cnt)\n   \n    \n# a = [1,2,3,4,5]\n# n = 5\n# for i in range(1,6):\n#     print(i)\n#     left = 0\n#     right = i-1\n#     subset = []\n#     s = sum(a[:right+1])\n#     subset.append(s)\n#     while right < n-1:\n#         right += 1\n#         s = s + a[right] - a[left]\n#         left += 1\n#         subset.append(s)\n\n#     print(subset)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13823