Chef is playing a game with two of his friends. In this game, each player chooses an integer between $1$ and $P$ inclusive. Let's denote the integers chosen by Chef, friend 1 and friend 2 by $i$, $j$ and $k$ respectively; then,  Chef's score is
(((Nmodi)modj)modk)modN.(((Nmodi)modj)modk)modN.(((N\,\mathrm{mod}\,i)\,\mathrm{mod}\,j)\,\mathrm{mod}\,k)\,\mathrm{mod}\,N\,.

Chef wants to obtain the maximum possible score. Let's denote this maximum score by $M$. Find the number of ways to choose the triple $(i,j,k)$ so that Chef's score is equal to $M$.

-----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 and only line of each test case contains two space-separated integers $N$ and $P$.

-----Output-----
For each test case, print a single line containing one integer — the number of ways to obtain the maximum score.

-----Constraints-----
- $1 \le T \le 10^6$
- $1 \le N \le P \le 10^6$

-----Subtasks-----
Subtask #1 (10 points):
- $1 \le T \le 100$
- $1 \le N \le P \le 100$
Subtask #2 (90 points): original constraints

-----Example Input-----
2
4 4
3 4

-----Example Output-----
9
13

-----Explanation-----
Example case 1: Chef's maximum possible score is $M = 1$. All possible values of $(i, j, k)$ such that the score is $1$ are
$(3, 2, 2)$,
$(3, 2, 3)$,
$(3, 2, 4)$,
$(3, 3, 2)$,
$(3, 3, 3)$,
$(3, 3, 4)$,
$(3, 4, 2)$,
$(3, 4, 3)$,
$(3, 4, 4)$.

```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 = 't = int(input())\nfor i in range(t) :\n n,p = map(int , input().split(" "))\n if n==1 or n==2 :\n  print(p*p*p)\n else :\n  if n%2 == 0 :\n   m = n//2 - 1\n   z = (p-m)*(p-m) + (p-n)*(p-m) + (p-n)*(p-n)\n  else :\n   m = n//2\n   z = (p - m) * (p - m) + (p - n) * (p - m) + (p - n) * (p - n)\n  print(z)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13149