Anas is playing an amazing game on a grid with $N$ rows and $M$ columns. The rows are numbered $1$ through $N$ from top to bottom and the columns are numbered $1$ through $M$ from left to right.
Anas wants to destroy this grid. To do that, he wants to send two heroes from the top left cell to the bottom right cell:
- The first hero visits cells in row-major order: $(1,1) \rightarrow (1,2) \rightarrow \ldots \rightarrow (1,M) \rightarrow (2,1) \rightarrow (2,2) \rightarrow \ldots \rightarrow (2,M) \rightarrow \ldots \rightarrow (N,M)$.
- The second hero visits cells in column-major order: $(1,1) \rightarrow (2,1) \rightarrow \ldots \rightarrow (N,1) \rightarrow (1,2) \rightarrow (2,2) \rightarrow \ldots \rightarrow (N,2) \rightarrow \ldots \rightarrow (N,M)$.
We know that each hero destroys the first cell he visits, rests in the next $K$ cells he visits without destroying them, then destroys the next cell he visits, rests in the next $K$ cells, destroys the next cell, and so on until he reaches (and rests in or destroys) the last cell he visits.
Anas does not know the value of $K$. Therefore, for each value of $K$ between $0$ and $N \cdot M - 1$ inclusive, he wants to calculate the number of cells that will be destroyed by at least one hero. Can you help him?

-----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 $M$.

-----Output-----
For each test case, print a single line containing $N \cdot M$ space-separated integers as described above.

-----Constraints-----
- $1 \le T \le 100$
- $2 \le N, M \le 1,000$
- the sum of $N \cdot M$ over all test cases does not exceed $2 \cdot 10^6$

-----Subtasks-----
Subtask #1 (30 points):
- $2 \le N, M \le 50$
- the sum of $N \cdot M$ over all test cases does not exceed $5,000$
Subtask #2 (70 points): original constraints

-----Example Input-----
1
2 3

-----Example Output-----
6 4 3 3 2 1

-----Explanation-----
Example case 1:
- $K = 0$: All cells will be destroyed by the heroes.
- $K = 1$: The first hero will destroy the cells $[(1,1), (1,3), (2,2)]$, while the second one will destroy the cells $[(1,1), (1,2), (1,3)]$.
- $K = 2$: The first hero will destroy the cells $[(1,1), (2,1)]$, while the second one will destroy the cells $[(1,1), (2,2)]$.
- $K = 3$: The first hero will destroy the cells $[(1,1), (2,2)]$, while the second one will destroy the cells $[(1,1), (1,3)]$.
- $K = 4$: The first hero will destroy the cells $[(1,1), (2,3)]$ and the second one will also destroy the cells $[(1,1), (2,3)]$.
- $K = 5$ : The first hero will destroy the cell $(1,1)$ and the second one will also destroy the cell $(1,1)$.

```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 = '"""\nCode chef problem DESTCELL, Destroy Cells\n"""\n\n\ndef find_destroyed_cells(cell_advance, n, m, k):\n row = 1\n col = 1\n destroyed_cells = {(1, 1)}\n while True:\n  row, col = cell_advance(row, col, n, m, k)\n  if row <= n and col <= m:\n   destroyed_cells.add((row, col))\n  else:\n   break\n return destroyed_cells\n\n\ndef cell_advance_hero1(row, col, n, m, k):\n return row + (col + k) // m, (col + k) % m + 1\n\n\ndef cell_advance_hero2(row, col, n, m, k):\n return (row + k) % n + 1, col + (row + k)//n\n\n\ndef main():\n t = int(input())\n for _ in range(t):\n  n, m = [int(s) for s in input().split(\' \')]\n  counts = []\n  for k in range(n*m):\n   cells_h1 = find_destroyed_cells(cell_advance_hero1, n, m, k)\n   cells_h2 = find_destroyed_cells(cell_advance_hero2, n, m, k)\n\n   destroyed = len(cells_h1) + len(cells_h2) - len(cells_h1 & cells_h2)\n   counts.append(destroyed)\n  print(\' \'.join([str(c) for c in counts]))\n\n\nmain()\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14175