You are given an unweighted tree with N$N$ nodes (numbered 1$1$ through N$N$). Let's denote the distance between any two nodes p$p$ and q$q$ by d(p,q)$d(p, q)$.
You should answer Q$Q$ queries. In each query, you are given parameters a$a$, da$d_a$, b$b$, db$d_b$, and you should find a node x$x$ such that d(x,a)=da$d(x, a) = d_a$ and d(x,b)=db$d(x, b) = d_b$, or determine that there is no such node.

-----Input-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
- The first line of each test case contains two space-separated integers N$N$ and Q$Q$.
- Each of the next N−1$N-1$ lines contains two space-separated integers u$u$ and v$v$ denoting that nodes u$u$ and v$v$ are connected by an edge.
- Each of the next Q$Q$ lines contains four space-separated integers a$a$, da$d_a$, b$b$ and db$d_b$ describing a query.

-----Output-----
For each query, print a single line containing one integer ― the number of a node satisfying the given requirements, or −1$-1$ if no such node exists.
If there are multiple solutions, you may output any one.

-----Constraints-----
- 1≤T≤1,000$1 \le T \le 1,000$
- 1≤N,Q≤106$1 \le N, Q \le 10^6$
- 1≤u,v≤N$1 \le u, v \le N$
- the graph on the input is a tree
- 1≤a,b≤N$1 \le a, b \le N$
- 1≤da,db<N$1 \le d_a, d_b < N$
- the sum of N$N$ over all test cases does not exceed 106$10^6$
- the sum of Q$Q$ over all test cases does not exceed 106$10^6$

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

-----Example Input-----
1
5 3
1 2
2 3
3 4
3 5
2 1 4 1
2 2 4 2
1 1 2 1

-----Example Output-----
3
5
-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 = '\n# cook your dish here\ndef dist(a,b):\n    if (a,b) in di :\n        return di[(a,b)]\n    if distance[a]<distance[b]:\n        a,b = b,a\n    c = distance[a] - distance[b]\n    t = a\n    while c:\n        t = p[t]\n        c -= 1\n    w = b\n    while t!=w:\n        t = p[t]\n        w = p[w]\n    di[(a,b)] = distance[a] + distance[b] - 2*distance[t]\n    return di[(a,b)]\n    \nt = int(input())\nfor t_iter in range(t):\n    n,q = map(int,input().split())\n    g = {}\n    for i in range(n):\n        g[i] = []\n    for i in range(n-1):\n        u,v = map(int,input().split())\n        g[u-1].append(v-1)\n        g[v-1].append(u-1)\n    \n    p = [None]*n\n    distance = [-1]*n\n    distance[0] = 0\n    qu= [0]\n    while len(qu):\n        u = qu.pop(0)\n        for v in g[u]:\n            if distance[v] == -1:\n                distance[v] = distance[u] + 1 \n                p[v] = u\n                qu.append(v)\n    # print(p)\n    # print(distance)\n    di = {}\n    for q_iter in range(q):\n        a,da,b,db = map(int,input().split())\n        a -= 1\n        b -= 1\n        flag = 0\n        for i in range(n):\n            if dist(a,i) == da and dist(b,i) == db :\n                print(i+1)\n                flag = 1\n                break\n        if flag == 0:\n            print(-1)\n                \n    \n        \n        '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13887