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>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fi first
#define se second
#define ll long long
#define ld long double
#define sz(x) ((int)(x).size())
#define all(x) 	(x).begin(), (x).end()
#define pb push_back
#define mpp make_pair
#define ve vector
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
const ll inf = 1e18; const int iinf = 1e9;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> inline bool chmin(T& a, T b) { return (a > b ? a = b, 1 : 0); }
template <typename T> inline bool chmax(T& a, T b) { return (a < b ? a = b, 1 : 0); }
const int N = 3e5 + 10;
const int M = 3e5 + 10;
ve<int> gr[N];
int n;
array<int,3> edges[M];
inline int go(const int &ID, const int &v) { return v ^ edges[ID][0] ^ edges[ID][1]; }
inline ve<ll> dij(const int &s) {
	ve<ll> d(n, inf); d[s] = 0;
	set<pll> st; st.insert({d[s], s});
	while (sz(st)) {
		int v = st.begin()->se;
		st.erase(st.begin());
		for (auto &id : gr[v]) {
			int to = go(id, v);
			int w = edges[id][2];
			if (d[to] > d[v] + w) {
				st.erase({d[to], to});
				d[to] = d[v] + w;
				st.insert({d[to], to});
			}
		}
	}
	return d;
}
inline void solve() {
	int m;
	cin >> n >> m;
	for (int i = 0; i < m; ++i) {
		int v, u, w;
		cin >> v >> u >> w;
		edges[i] = {--v, --u, w};
		gr[v].pb(i);
		gr[u].pb(i);
	}
	ve<int> sf(m);
	for (int i = m - 2; ~i; --i) {
		sf[i] = max(sf[i + 1], edges[i + 1][2]);
	}
	auto d0 = dij(0);
	auto d1 = dij(n - 1);
	auto can = [&](const ll &x) -> bool {
		int timer = 0;
		ve<int> in(n), up(n), used(n);
		bool ok = 0;
		function<void(int,int)> dfs = [&](int v, int pid) {
			used[v] = 1;
			in[v] = up[v] = timer++;
			for (auto &id : gr[v]) {
				int to = go(id, v);
				auto &[A, B, w] = edges[id];
				ll cs = min(d0[A] + d1[B], d1[A] + d0[B]) + w;
				if (cs > x || id == pid) continue;
				if (used[to] == 1) {
					chmin(up[v], in[to]);
				}
				else if (!used[to]) {
					dfs(to, id);
					chmin(up[v], up[to]);
					if (up[to] > in[v] && in[n - 1] >= in[to] && cs + sf[id] > x) {
						ok = 1;
					}
				}
			}
			used[v] = 2;
		};
		dfs(0, -1);
		return ok;
	};
	ll l = d0[n - 1];
	ll r = d0[n - 1] + sf[0] + 10;
	while (l < r) {
		ll mid = l + r >> 1;
		if (can(mid)) l = mid + 1;
		else r = mid;
	}
	cout << l;
}
signed main() {
	ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
	int q = 1; // cin >> q;
	while (q--) solve();
	cerr << fixed << setprecision(3) << "Time execution: " << (double)clock() / CLOCKS_PER_SEC << endl;
}
Compilation message (stderr)
Aesthetic.cpp: In function 'void solve()':
Aesthetic.cpp:119:14: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  119 |   ll mid = l + r >> 1;
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