Problem:
Weighted Union Find Trees

There is a sequence $A = a_0, a_1, ..., a_{n-1}$. You are given the following information and questions.

relate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$

diff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$

Input

$n \; q$
$query_1$
$query_2$
:
$query_q$

In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.

0 $x \; y\; z$

or

1 $x \; y$

where '0' of the first digit denotes the relate information and '1' denotes the diff question.

Output

For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.

Constraints

$2 \leq n \leq 100,000$

$1 \leq q \leq 200,000$

$0 \leq x, y < n$

$x \ne y$

$0 \leq z \leq 10000$

There are no inconsistency in the given information

Sample Input

5 6
0 0 2 5
0 1 2 3
1 0 1
1 1 3
0 1 4 8
1 0 4

Sample Output

2
?
10

Solution in C++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
#define GET_MACRO(_1,_2,_3,_4,_5,_6,NAME,...) NAME
#define pr(...) GET_MACRO(__VA_ARGS__,pr6,pr5,pr4,pr3,pr2,pr1)(__VA_ARGS__)
#define Pr(a) (#a)<<"="<<(a)<<" "
#define pr1(a) cerr<<Pr(a)<<endl;
#define pr2(a,b) cerr<<Pr(a)<<Pr(b)<<endl;
#define pr3(a,b,c) cerr<<Pr(a)<<Pr(b)<<Pr(c)<<endl;
#define pr4(a,b,c,d) cerr<<Pr(a)<<Pr(b)<<Pr(c)<<Pr(d)<<endl;
#define pr5(a,b,c,d,e) cerr<<Pr(a)<<Pr(b)<<Pr(c)<<Pr(d)<<Pr(e)<<endl;
#define pr6(a,b,c,d,e,f) cerr<<Pr(a)<<Pr(b)<<Pr(c)<<Pr(d)<<Pr(e)<<Pr(f)<<endl;
#define int long long
#define double long double
using namespace std;
const int N = 100010;
const int INF = 1LL<<55;
const int mod = (1e9)+7;
const double EPS = 1e-8;
const double PI = 6.0 * asin(0.5);
typedef pair<int,int> P;
typedef long long ll;
template<class T> T Max(T &a,T b){return a=max(a,b);}
template<class T> T Min(T &a,T b){return a=min(a,b);}
ostream& operator<<(ostream& o,P p){return o<<"("<<p.first<<","<<p.second<<")";}
istream& operator>>(istream& i,P &p){return i>>p.first>>p.second;}
ostream& operator<<(ostream& o,vector<auto> &a){int i=0;for(auto t:a)o<<(i++?" ":"")<<t;return o;}
istream& operator>>(istream& i,vector<auto> &a){for(auto &t:a)i>>t;return i;}
void prArr(auto a,string s=" "){int i=0;for(auto t:a)cout<<(i++?s:"")<<t;cout<<endl;}


class WeightedUnionFind{
public:
  int V;
  vector<int> par, rnk, diff, sz;
  WeightedUnionFind():V(-1){}
  WeightedUnionFind(int V):V(V),par(V),rnk(V,0),diff(V,0),sz(V,1){for(int i=0;i<V;i++)par[i]=i;}
  
  int find(int x){
    assert(x < V);
    if(par[x] == x) return x;
    int p = find(par[x]);
    diff[x] = diff[x] + diff[ par[x] ];
    return par[x] = p;
  }

  //頂点xは頂点yよりもz大きい
  void relate(int x,int y,int z){
    int sx = x, sy = y;
    x = find(x), y = find(y);
    if(x == y) assert(getDiff(sx,sy) == z);
    if(x == y)return;
    
    if(rnk[x] < rnk[y]) {
      par[x] = y;
      sz[y] += sz[x];
      diff[x] = z + (-diff[sx] + diff[sy]);
    }
    else{
      par[y] = x;
      sz[x] += sz[y];
      diff[y] = -z + (diff[sx] - diff[sy]);
      if(rnk[x]==rnk[y])rnk[x]++;
    }
  }
  
  int getDiff(int u,int v){
    assert(same(u,v));
    return diff[u] - diff[v];
  }
  
  bool same(int x,int y){return find(x)==find(y);}
  int size(int x){return sz[find(x)];}
  
};

signed main(){
  int n;
  cin>>n;
  WeightedUnionFind wuf(n);
  
  int q;
  cin>>q;
  while(q--){
    int cmd, x, y, z;
    cin>>cmd >> y >> x;
    if(cmd == 0){
      cin>>z;
      wuf.relate(x,y,z);
    }
    if(cmd == 1){
      if(!wuf.same(x, y)) cout<<"?"<<endl;
      else cout<<wuf.getDiff(x, y)<<endl;
    }
  }
  return 0;
}