This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	int n,m;cin>>n>>m;
	int S,T;cin>>S>>T;
	--S;--T;
	int U,V;cin>>U>>V;
	--U;--V;
	vector<vector<pair<int,long long>>>adj(n);
	for (int i = 0;i<m;++i){
		int x,y,z;cin>>x>>y>>z;
		--x;--y;
		adj[x].push_back({y,z});
		adj[y].push_back({x,z});
	}
	const long long mxn = 1e15;
	priority_queue<pair<long long,pair<int,int>>>q;
	vector<vector<long long>>dist(n,vector<long long>(2,mxn));
	q.push({0,{U,0}});
	q.push({0,{V,1}});
	dist[U][0] = 0;
	dist[V][1] = 0;
	while(!q.empty()){
		auto u = q.top().second;
		q.pop();
		for (auto x:adj[u.first]){
			if (dist[x.first][u.second] > dist[u.first][u.second] + x.second){
				dist[x.first][u.second] = dist[u.first][u.second] + x.second;
				q.push({-dist[x.first][u.second],{x.first,u.second}});
			}
		}
	}
	vector<int>visited(n,0);
	long long ans = dist[U][1];
	vector<long long>dis(n,mxn);
	auto bfs = [&](){
		priority_queue<pair<long long,int>>qq;
		qq.push({0,S});
		dis[S] = 0;
		while(!qq.empty()){
			auto u = qq.top().second;
			qq.pop();
			for (auto x:adj[u]){
				if (dis[x.first] > dis[u] + x.second){
					dis[x.first] = dis[u] + x.second;
					qq.push({-dis[x.first],x.first});
				}
			}
		}
	};
	vector<pair<long long,long long>>dp(n,{mxn,mxn});
	bfs();
	function<pair<long long,long long>(int,long long,long long,long long)>dfs = [&](int u,long long dd,long long pp,long long bb){
		if (u == T){
			return make_pair(pp,bb);
		}
		pair<long long,long long> pu = make_pair(mxn,mxn);
		if (dp[u]!=make_pair(mxn,mxn))return dp[u];
		for (auto x:adj[u]){
			if (dd + x.second <=dis[x.first] && !visited[x.first]){
				visited[x.first] = true;
				pair<long long,long long>v = dfs(x.first,dd + x.second,min(pp,dist[x.first][0]),min(dist[x.first][1],bb));
				if (v.first + v.second < pu.first + pu.second){
					pu = v;
				}
			}
		}
		return dp[u] = pu;
	};
	auto x = dfs(S,0,dist[S][0],dist[S][1]);
	ans = min(ans,x.first + x.second);
	cout<<ans<<'\n';
	return 0;
}
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