It is an interesting exercise to write a program to print out all permutations of $1, 2, …, n$. However, since there are $6227020800$ permutations of $1, 2, …, 13$, it is unlikely that we would ever run this program on an input of size more than $10$.
However, here is another interesting problem whose solution can also be used to generate permutations. We can order the permutations of $1, 2, …, n$ under the lexicographic (or dictionary) order. Here are the permutations of $1,2,3$ in lexicographic order:
123132213231312321123132213231312321 1 \, 2 \, 3 \quad    1 \, 3 \, 2 \quad     2 \, 1 \, 3 \quad     2 \, 3 \, 1 \quad     3 \, 1 \, 2 \quad     3 \, 2 \, 1 
The problem we have is the following: given a permutation of $1,2, …, n$, generate the next permutation in lexicographic order. For example, for $2 3 1 4$ the answer is $2 3 4 1$.

-----Input:-----
The first line of the input contains two integers, $N$ and $K$. This is followed by $K$ lines, each of which contains one permutation of $1, 2,…,N$.

-----Output:-----
The output should consist of $K$ lines. Line $i$ should contain the lexicographically next permutation correponding to the permutation on line $i+1$ in the input.

-----Constraints:-----
- $1 \leq N \leq 1000$.
- $1 \leq K \leq 10$.

-----Sample input-----
3 2
3 1 2
2 3 1

-----Sample output-----
3 2 1
3 1 2

```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 sys\n# import math as mt\n# from collections import Counter\n# from itertools import permutations\n# from functools import reduce\n# from heapq import nsmallest, nlargest, heapify, heappop, heappush, heapreplace\n\ndef get_inpt(): return sys.stdin.readline().strip()\ndef get_int(): return int(sys.stdin.readline().strip())\ndef get_ints(): return map(int, sys.stdin.readline().strip().split())\ndef get_array(): return list(map(int, sys.stdin.readline().strip().split()))\n\n# sys.setrecursionlimit(10**7)\n# INF = float('inf')\n# MOD1, MOD2 = 10**9+7, 998244353\n\nn, k = get_ints()\n\nfor _ in range(k):\n    \n    arr = get_array()\n    \n    for i in reversed(range(n-1)):\n        \n        if arr[i] < arr[i+1]:\n            \n            ind = i+1\n            minn = arr[i+1]\n            for j in range(i+1, n):\n                if arr[j] > arr[i]:\n                    minn = min(arr[j], minn)\n                    ind = j\n                    \n            arr[i], arr[ind] = arr[ind], arr[i]\n            \n            arr = arr[:i+1] + sorted(arr[i+1:])\n            \n            break\n    \n    print(*arr)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14243