#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5, mod = 1e9 + 7, inf = mod + 10ll;
int n, m, a[maxn], ans[maxn], tme, st[maxn], ft[maxn], blp[maxn], h[maxn],
    par[20][maxn], mx[20][maxn], pw2[20], p[maxn], sz[maxn], ip[maxn], mn[maxn],
    seg[maxn * 4ll], lzy[maxn * 4ll];
vector<pair<int, int>> v1[maxn], v2[maxn];
vector<pair<int, pair<int, int>>> adj[maxn], g[maxn];
vector<pair<pair<int, int>, pair<int, int>>> vec;
set<pair<int, int>> s[maxn];
bool mrk[maxn];
int get_par(int u) {
  if (p[u] == 0) return u;
  return p[u] = get_par(p[u]);
}
bool merge(int u, int v) {
  u = get_par(u);
  v = get_par(v);
  if (u == v) return 0;
  if (sz[u] < sz[v]) swap(u, v);
  p[v] = u;
  sz[u] += sz[v];
  return 1;
}
void dfs12(int u) {
  for (int i = 1; i < 20; i++) {
    int v = par[i - 1][u];
    if ((v == 0) || (par[i - 1][v] == 0)) break;
    par[i][u] = par[i - 1][v];
    mx[i][u] = max(mx[i - 1][u], mx[i - 1][v]);
  }
  for (auto j : g[u]) {
    int v = j.first, w = j.second.first;
    if (j.first == par[0][u]) continue;
    ip[v] = j.second.second;
    mx[0][v] = w;
    par[0][v] = u;
    h[v] = h[u] + 1;
    dfs12(v);
  }
}
void build_mst() {
  sort(vec.begin(), vec.end());
  for (auto i : vec) {
    int u = i.second.first, v = i.second.second, w = i.first.first;
    if (merge(u, v)) {
      g[u].push_back({v, {w, i.first.second}});
      g[v].push_back({u, {w, i.first.second}});
      mrk[i.first.second] = 1;
    }
  }
  dfs12(1);
}
int get_pr(int v, int d) {
  for (int i = 0; i < 20; i++) {
    if ((pw2[i] & d) == 0) continue;
    v = par[i][v];
  }
  return v;
}
int get_mx(int v, int d) {
  int MX = 0;
  for (int i = 0; i < 20; i++) {
    if ((pw2[i] & d) == 0) continue;
    MX = max(MX, mx[i][v]);
    v = par[i][v];
  }
  return MX;
}
int get_lca(int u, int v) {
  if (h[u] > h[v]) swap(u, v);
  if (h[u] != h[v]) v = get_pr(v, h[v] - h[u]);
  if (u == v) return u;
  for (int i = 19; i >= 0; i--) {
    if (par[i][v] == par[i][u]) continue;
    u = par[i][u];
    v = par[i][v];
  }
  return par[0][u];
}
void fix_tree(int u, int prr) {
  sz[u] = 1;
  pair<int, pair<int, int>> big = {-1, {-1, -1}};
  for (auto j : g[u]) {
    if (j.first == prr) continue;
    fix_tree(j.first, u);
    if (big.first == -1)
      big = j;
    else if (sz[big.first] < sz[j.first])
      big = j;
  }
  if (big.first == -1) {
    g[u].clear();
    return;
  }
  vector<pair<int, pair<int, int>>> g2;
  g2.push_back(big);
  for (auto j : g[u]) {
    if (j.first == prr) continue;
    if (j.first == big.first) continue;
    g2.push_back(j);
  }
  g[u] = g2;
}
void dfs(int u) {
  st[u] = tme;
  tme++;
  int big = 0;
  if (g[u].size()) big = g[u][0].first;
  for (auto j : g[u]) {
    if (j.first == big)
      blp[big] = blp[u];
    else
      blp[j.first] = j.first;
    dfs(j.first);
  }
  ft[u] = tme;
}
void shift(int v, int s, int e) {
  int x = lzy[v], lc = v << 1, rc = lc | 1;
  seg[lc] = min(seg[lc], x);
  seg[rc] = min(seg[rc], x);
  lzy[lc] = min(lzy[lc], x);
  lzy[rc] = min(lzy[rc], x);
}
int get(int l, int r, int v = 1, int s = 0, int e = n) {
  if ((l >= e) || (r <= s)) return inf;
  if ((l <= s) && (e <= r)) return seg[v];
  shift(v, s, e);
  int mid = (e + s) >> 1, lc = v << 1, rc = lc | 1;
  return min(get(l, r, lc, s, mid), get(l, r, rc, mid, e));
}
void fix(int l, int r, int x, int v = 1, int s = 0, int e = n) {
  if ((l >= e) || (r <= s)) return;
  if ((l <= s) && (e <= r)) {
    seg[v] = min(seg[v], x);
    lzy[v] = min(lzy[v], x);
    return;
  }
  int mid = (e + s) >> 1, lc = v << 1, rc = lc | 1;
  fix(l, r, x, lc, s, mid);
  fix(l, r, x, rc, mid, e);
  seg[v] = min(seg[lc], seg[rc]);
}
void fix_path(int lca, int v, int w) {
  if (v == lca) return;
  if (blp[v] == v) {
    ans[ip[v]] = min(ans[ip[v]], w);
    fix_path(lca, par[0][v], w);
    return;
  }
  if (h[lca] <= h[blp[v]]) {
    fix(st[blp[v]] + 1, st[v] + 1, w);
    fix_path(lca, blp[v], w);
    return;
  }
  fix(st[lca] + 1, st[v] + 1, w);
  return;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  pw2[0] = 1;
  for (int i = 1; i < 20; i++) pw2[i] = (pw2[i - 1] * 2ll);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    adj[u].push_back({v, {w, i}});
    adj[v].push_back({u, {w, i}});
    vec.push_back({{w, i}, {u, v}});
  }
  build_mst();
  for (auto j : vec) {
    int u = j.second.first, v = j.second.second, w = j.first.first,
        i = j.first.second;
    if (h[u] > h[v]) swap(u, v);
    if (par[0][v] == u) {
      ans[i] = inf;
      continue;
    }
    int lca = get_lca(u, v);
    v1[u].push_back({w, v});
    v1[v].push_back({w, u});
    v2[lca].push_back({w, v});
    v2[lca].push_back({w, u});
    ans[i] = max(get_mx(u, h[u] - h[lca]), get_mx(v, h[v] - h[lca])) - 1;
  }
  tme = 0;
  fix_tree(1, 1);
  blp[1] = 1;
  dfs(1);
  fill(seg, seg + maxn * 4ll, inf);
  fill(lzy, lzy + maxn * 4ll, inf);
  for (auto j : vec) {
    int u = j.second.first, v = j.second.second, w = j.first.first - 1ll,
        i = j.first.second;
    if (h[u] > h[v]) swap(u, v);
    if (par[0][v] == u) continue;
    int lca = get_lca(u, v);
    fix_path(lca, u, w);
    fix_path(lca, v, w);
  }
  for (int i = 2; i <= n; i++)
    ans[ip[i]] = min(get(st[i], st[i] + 1ll), ans[ip[i]]);
  for (int i = 0; i < m; i++) {
    if (ans[i] > mod) ans[i] = -1;
    cout << ans[i] << ' ';
  }
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

You are given a connected weighted graph with n vertices and m edges. The graph doesn't contain loops nor multiple edges. Consider some edge with id i. Let's determine for this edge the maximum integer weight we can give to it so that it is contained in all minimum spanning trees of the graph if we don't change the other weights.

You are to determine this maximum weight described above for each edge. You should calculate the answer for each edge independently, it means there can't be two edges with changed weights at the same time.

Input

The first line contains two integers n and m (2 ≤ n ≤ 2·105, n - 1 ≤ m ≤ 2·105), where n and m are the number of vertices and the number of edges in the graph, respectively.

Each of the next m lines contains three integers u, v and c (1 ≤ v, u ≤ n, v ≠ u, 1 ≤ c ≤ 109) meaning that there is an edge between vertices u and v with weight c. 

Output

Print the answer for each edge in the order the edges are given in the input. If an edge is contained in every minimum spanning tree with any weight, print -1 as the answer.

Examples

Input

4 4
1 2 2
2 3 2
3 4 2
4 1 3


Output

2 2 2 1 

Input

4 3
1 2 2
2 3 2
3 4 2


Output

-1 -1 -1 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5, mod = 1e9 + 7, inf = mod + 10ll;
int n, m, a[maxn], ans[maxn], tme, st[maxn], ft[maxn], blp[maxn], h[maxn],
    par[20][maxn], mx[20][maxn], pw2[20], p[maxn], sz[maxn], ip[maxn], mn[maxn],
    seg[maxn * 4ll], lzy[maxn * 4ll];
vector<pair<int, int>> v1[maxn], v2[maxn];
vector<pair<int, pair<int, int>>> adj[maxn], g[maxn];
vector<pair<pair<int, int>, pair<int, int>>> vec;
set<pair<int, int>> s[maxn];
bool mrk[maxn];
int get_par(int u) {
  if (p[u] == 0) return u;
  return p[u] = get_par(p[u]);
}
bool merge(int u, int v) {
  u = get_par(u);
  v = get_par(v);
  if (u == v) return 0;
  if (sz[u] < sz[v]) swap(u, v);
  p[v] = u;
  sz[u] += sz[v];
  return 1;
}
void dfs12(int u) {
  for (int i = 1; i < 20; i++) {
    int v = par[i - 1][u];
    if ((v == 0) || (par[i - 1][v] == 0)) break;
    par[i][u] = par[i - 1][v];
    mx[i][u] = max(mx[i - 1][u], mx[i - 1][v]);
  }
  for (auto j : g[u]) {
    int v = j.first, w = j.second.first;
    if (j.first == par[0][u]) continue;
    ip[v] = j.second.second;
    mx[0][v] = w;
    par[0][v] = u;
    h[v] = h[u] + 1;
    dfs12(v);
  }
}
void build_mst() {
  sort(vec.begin(), vec.end());
  for (auto i : vec) {
    int u = i.second.first, v = i.second.second, w = i.first.first;
    if (merge(u, v)) {
      g[u].push_back({v, {w, i.first.second}});
      g[v].push_back({u, {w, i.first.second}});
      mrk[i.first.second] = 1;
    }
  }
  dfs12(1);
}
int get_pr(int v, int d) {
  for (int i = 0; i < 20; i++) {
    if ((pw2[i] & d) == 0) continue;
    v = par[i][v];
  }
  return v;
}
int get_mx(int v, int d) {
  int MX = 0;
  for (int i = 0; i < 20; i++) {
    if ((pw2[i] & d) == 0) continue;
    MX = max(MX, mx[i][v]);
    v = par[i][v];
  }
  return MX;
}
int get_lca(int u, int v) {
  if (h[u] > h[v]) swap(u, v);
  if (h[u] != h[v]) v = get_pr(v, h[v] - h[u]);
  if (u == v) return u;
  for (int i = 19; i >= 0; i--) {
    if (par[i][v] == par[i][u]) continue;
    u = par[i][u];
    v = par[i][v];
  }
  return par[0][u];
}
void fix_tree(int u, int prr) {
  sz[u] = 1;
  pair<int, pair<int, int>> big = {-1, {-1, -1}};
  for (auto j : g[u]) {
    if (j.first == prr) continue;
    fix_tree(j.first, u);
    if (big.first == -1)
      big = j;
    else if (sz[big.first] < sz[j.first])
      big = j;
  }
  if (big.first == -1) {
    g[u].clear();
    return;
  }
  vector<pair<int, pair<int, int>>> g2;
  g2.push_back(big);
  for (auto j : g[u]) {
    if (j.first == prr) continue;
    if (j.first == big.first) continue;
    g2.push_back(j);
  }
  g[u] = g2;
}
void dfs(int u) {
  st[u] = tme;
  tme++;
  int big = 0;
  if (g[u].size()) big = g[u][0].first;
  for (auto j : g[u]) {
    if (j.first == big)
      blp[big] = blp[u];
    else
      blp[j.first] = j.first;
    dfs(j.first);
  }
  ft[u] = tme;
}
void shift(int v, int s, int e) {
  int x = lzy[v], lc = v << 1, rc = lc | 1;
  seg[lc] = min(seg[lc], x);
  seg[rc] = min(seg[rc], x);
  lzy[lc] = min(lzy[lc], x);
  lzy[rc] = min(lzy[rc], x);
}
int get(int l, int r, int v = 1, int s = 0, int e = n) {
  if ((l >= e) || (r <= s)) return inf;
  if ((l <= s) && (e <= r)) return seg[v];
  shift(v, s, e);
  int mid = (e + s) >> 1, lc = v << 1, rc = lc | 1;
  return min(get(l, r, lc, s, mid), get(l, r, rc, mid, e));
}
void fix(int l, int r, int x, int v = 1, int s = 0, int e = n) {
  if ((l >= e) || (r <= s)) return;
  if ((l <= s) && (e <= r)) {
    seg[v] = min(seg[v], x);
    lzy[v] = min(lzy[v], x);
    return;
  }
  int mid = (e + s) >> 1, lc = v << 1, rc = lc | 1;
  fix(l, r, x, lc, s, mid);
  fix(l, r, x, rc, mid, e);
  seg[v] = min(seg[lc], seg[rc]);
}
void fix_path(int lca, int v, int w) {
  if (v == lca) return;
  if (blp[v] == v) {
    ans[ip[v]] = min(ans[ip[v]], w);
    fix_path(lca, par[0][v], w);
    return;
  }
  if (h[lca] <= h[blp[v]]) {
    fix(st[blp[v]] + 1, st[v] + 1, w);
    fix_path(lca, blp[v], w);
    return;
  }
  fix(st[lca] + 1, st[v] + 1, w);
  return;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  pw2[0] = 1;
  for (int i = 1; i < 20; i++) pw2[i] = (pw2[i - 1] * 2ll);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    adj[u].push_back({v, {w, i}});
    adj[v].push_back({u, {w, i}});
    vec.push_back({{w, i}, {u, v}});
  }
  build_mst();
  for (auto j : vec) {
    int u = j.second.first, v = j.second.second, w = j.first.first,
        i = j.first.second;
    if (h[u] > h[v]) swap(u, v);
    if (par[0][v] == u) {
      ans[i] = inf;
      continue;
    }
    int lca = get_lca(u, v);
    v1[u].push_back({w, v});
    v1[v].push_back({w, u});
    v2[lca].push_back({w, v});
    v2[lca].push_back({w, u});
    ans[i] = max(get_mx(u, h[u] - h[lca]), get_mx(v, h[v] - h[lca])) - 1;
  }
  tme = 0;
  fix_tree(1, 1);
  blp[1] = 1;
  dfs(1);
  fill(seg, seg + maxn * 4ll, inf);
  fill(lzy, lzy + maxn * 4ll, inf);
  for (auto j : vec) {
    int u = j.second.first, v = j.second.second, w = j.first.first - 1ll,
        i = j.first.second;
    if (h[u] > h[v]) swap(u, v);
    if (par[0][v] == u) continue;
    int lca = get_lca(u, v);
    fix_path(lca, u, w);
    fix_path(lca, v, w);
  }
  for (int i = 2; i <= n; i++)
    ans[ip[i]] = min(get(st[i], st[i] + 1ll), ans[ip[i]]);
  for (int i = 0; i < m; i++) {
    if (ans[i] > mod) ans[i] = -1;
    cout << ans[i] << ' ';
  }
}

```