Chef has two integer sequences $A_1, A_2, \ldots, A_N$ and $B_1, B_2, \ldots, B_M$. You should choose $N+M-1$ pairs, each in the form $(A_x, B_y)$, such that the sums $A_x + B_y$ are all pairwise distinct.
It is guaranteed that under the given constraints, a solution always exists. If there are multiple solutions, you may find any one.

-----Input-----
- The first line of the input contains two space-separated integers $N$ and $M$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- The third line contains $M$ space-separated integers $B_1, B_2, \ldots, B_M$.

-----Output-----
Print $N+M-1$ lines. Each of these lines should contain two space-separated integers $x$ and $y$ denoting that you chose a pair $(A_{x+1}, B_{y+1})$.

-----Constraints-----
- $1 \le N, M \le 2 \cdot 10^5$
- $|A_i| \le 10^9$ for each valid $i$
- $|B_i| \le 10^9$ for each valid $i$
- $A_1, A_2, \ldots, A_N$ are pairwise distinct
- $B_1, B_2, \ldots, B_M$ are pairwise distinct

-----Subtasks-----
Subtask #1 (25 points): $1 \le N, M \le 10^3$
Subtask #2 (75 points): original constraints

-----Example Input-----
3 2
10 1 100
4 3

-----Example Output-----
2 1
0 0
1 0
0 1

-----Explanation-----
The chosen pairs and their sums are:
- $A_3 + B_2 = 100+3 = 103$
- $A_1 + B_1 = 10+4 = 14$
- $A_2 + B_1 = 1+4 = 5$
- $A_1 + B_2 = 10+3 = 13$
Since all sums are distinct, this is a correct output.

```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 = "N,M = [int(i) for i in input().split()]\nA = [int(i) for i in input().split()]\nB = [int(i) for i in input().split()]\n\nans = []\n\nseen = {}\nflag = False\n\nfor i in range(N):\n    for j in range(M):\n        if(len(ans)==N+M-1):\n            flag = True\n            break\n        if(A[i]+B[j] not in seen):\n            ans.append('{} {}'.format(i,j))\n            seen[A[i]+B[j]] = True\n    if(flag):\n        break\n\nfor i in ans:\n    print(i)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13443