#include <bits/stdc++.h>
using namespace std;
namespace Dango {
const int MAXN = 200005, INF = 0x3f3f3f3f;
struct Edge {
  int from, to, dis, id;
  bool operator<(const Edge b) const { return dis < b.dis; }
} e[MAXN];
struct tree {
  int l, r, data;
  bool tag;
} t[MAXN << 2];
int n, m;
int head[MAXN], to[MAXN * 2], dis[MAXN * 2], nxt[MAXN * 2];
int fa[MAXN];
int ans[MAXN];
int size[MAXN], maxson[MAXN], belong[MAXN], f[MAXN];
int id[MAXN], link[MAXN], tmp[MAXN], d[MAXN];
bool flag[MAXN];
int read() {
  int x = 0, f = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    f |= (ch == '-');
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return f ? -x : x;
}
int ffind(int a) { return f[a] == a ? a : f[a] = ffind(f[a]); }
void add(int u, int v, int w) {
  static int cnt;
  cnt++;
  to[cnt] = v;
  dis[cnt] = w;
  nxt[cnt] = head[u];
  head[u] = cnt;
}
void dfs1(int u, int f) {
  size[u] = 1;
  fa[u] = f;
  d[u] = d[f] + 1;
  for (int i = head[u]; i; i = nxt[i]) {
    int v = to[i];
    if (v == f) continue;
    tmp[v] = dis[i];
    dfs1(v, u);
    size[u] += size[v];
    if (size[v] > size[maxson[u]]) maxson[u] = v;
  }
}
void dfs2(int u, int f, int anc) {
  static int cnt;
  id[u] = ++cnt;
  link[cnt] = u;
  belong[u] = anc;
  if (maxson[u]) dfs2(maxson[u], u, anc);
  for (int i = head[u]; i; i = nxt[i]) {
    int v = to[i];
    if (v == f || v == maxson[u]) continue;
    dfs2(v, u, v);
  }
}
void build(int a, int l, int r) {
  t[a].l = l;
  t[a].r = r;
  t[a].tag = false;
  if (l == r) {
    t[a].data = tmp[link[l]];
    return;
  }
  int mid = (l + r) >> 1;
  build(a << 1, l, mid);
  build(a << 1 | 1, mid + 1, r);
  t[a].data = max(t[a << 1].data, t[a << 1 | 1].data);
}
void pushdown(int a) {
  int l = a << 1, r = a << 1 | 1;
  t[a].tag = false;
  t[l].data = min(t[l].data, t[a].data);
  t[r].data = min(t[r].data, t[a].data);
  t[l].tag = t[r].tag = true;
}
void update(int a, int l, int r, int data) {
  if (t[a].l >= l && t[a].r <= r) {
    t[a].data = min(t[a].data, data);
    t[a].tag = true;
    return;
  }
  if (t[a].tag) pushdown(a);
  int mid = (t[a].l + t[a].r) >> 1;
  if (l <= mid) update(a << 1, l, r, data);
  if (r > mid) update(a << 1 | 1, l, r, data);
}
int querymax(int a, int l, int r) {
  if (t[a].l >= l && t[a].r <= r) return t[a].data;
  if (t[a].tag) pushdown(a);
  int mid = (t[a].l + t[a].r) >> 1, res = 0;
  if (l <= mid) res = max(res, querymax(a << 1, l, r));
  if (r > mid) res = max(res, querymax(a << 1 | 1, l, r));
  return res;
}
int querymin(int a, int l, int r) {
  if (t[a].l >= l && t[a].r <= r) return t[a].data;
  if (t[a].tag) pushdown(a);
  int mid = (t[a].l + t[a].r) >> 1, res = INF;
  if (l <= mid) res = min(res, querymin(a << 1, l, r));
  if (r > mid) res = min(res, querymin(a << 1 | 1, l, r));
  return res;
}
int solve(int u, int v) {
  int res = 0;
  while (belong[u] != belong[v]) {
    if (d[belong[u]] < d[belong[v]]) swap(u, v);
    res = max(res, querymax(1, id[belong[u]], id[u]));
    u = fa[belong[u]];
  }
  if (u != v) {
    if (d[u] > d[v]) swap(u, v);
    res = max(res, querymax(1, id[u] + 1, id[v]));
  }
  return res - 1;
}
void fix(int u, int v, int w) {
  while (belong[u] != belong[v]) {
    if (d[belong[u]] < d[belong[v]]) swap(u, v);
    update(1, id[belong[u]], id[u], w);
    u = fa[belong[u]];
  }
  if (u != v) {
    if (d[u] > d[v]) swap(u, v);
    update(1, id[u] + 1, id[v], w);
  }
}
int solve2(int u, int v) {
  int res = INF;
  while (belong[u] != belong[v]) {
    if (d[belong[u]] < d[belong[v]]) swap(u, v);
    res = min(res, querymin(1, id[belong[u]], id[u]));
    u = fa[belong[u]];
  }
  if (u != v) {
    if (d[u] > d[v]) swap(u, v);
    res = min(res, querymin(1, id[u] + 1, id[v]));
  }
  if (res == INF) res = 0;
  return res - 1;
}
int work() {
  n = read();
  m = read();
  for (int i = 1; i <= n; i++) f[i] = i;
  for (int i = 1; i <= m; i++) {
    e[i].from = read();
    e[i].to = read();
    e[i].dis = read();
    e[i].id = i;
  }
  sort(e + 1, e + m + 1);
  for (int i = 1; i <= m; i++) {
    int u = e[i].from, v = e[i].to, w = e[i].dis;
    int a = ffind(u), b = ffind(v);
    if (a != b) {
      f[a] = b;
      add(u, v, w);
      add(v, u, w);
    } else
      flag[i] = true;
  }
  dfs1(1, 0);
  dfs2(1, 0, 1);
  build(1, 1, n);
  for (int i = 1; i <= m; i++) {
    if (!flag[i]) continue;
    ans[e[i].id] = solve(e[i].from, e[i].to);
  }
  memset(tmp, INF, sizeof(tmp));
  build(1, 1, n);
  for (int i = 1; i <= m; i++) {
    if (!flag[i]) continue;
    fix(e[i].from, e[i].to, e[i].dis);
  }
  for (int i = 1; i <= m; i++) {
    if (flag[i]) continue;
    ans[e[i].id] = solve2(e[i].from, e[i].to);
  }
  for (int i = 1; i <= m; i++) printf("%d ", ans[i]);
  return 0;
}
}  // namespace Dango
int main() { return Dango::work(); }

### Prompt

Generate 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;
namespace Dango {
const int MAXN = 200005, INF = 0x3f3f3f3f;
struct Edge {
  int from, to, dis, id;
  bool operator<(const Edge b) const { return dis < b.dis; }
} e[MAXN];
struct tree {
  int l, r, data;
  bool tag;
} t[MAXN << 2];
int n, m;
int head[MAXN], to[MAXN * 2], dis[MAXN * 2], nxt[MAXN * 2];
int fa[MAXN];
int ans[MAXN];
int size[MAXN], maxson[MAXN], belong[MAXN], f[MAXN];
int id[MAXN], link[MAXN], tmp[MAXN], d[MAXN];
bool flag[MAXN];
int read() {
  int x = 0, f = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    f |= (ch == '-');
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return f ? -x : x;
}
int ffind(int a) { return f[a] == a ? a : f[a] = ffind(f[a]); }
void add(int u, int v, int w) {
  static int cnt;
  cnt++;
  to[cnt] = v;
  dis[cnt] = w;
  nxt[cnt] = head[u];
  head[u] = cnt;
}
void dfs1(int u, int f) {
  size[u] = 1;
  fa[u] = f;
  d[u] = d[f] + 1;
  for (int i = head[u]; i; i = nxt[i]) {
    int v = to[i];
    if (v == f) continue;
    tmp[v] = dis[i];
    dfs1(v, u);
    size[u] += size[v];
    if (size[v] > size[maxson[u]]) maxson[u] = v;
  }
}
void dfs2(int u, int f, int anc) {
  static int cnt;
  id[u] = ++cnt;
  link[cnt] = u;
  belong[u] = anc;
  if (maxson[u]) dfs2(maxson[u], u, anc);
  for (int i = head[u]; i; i = nxt[i]) {
    int v = to[i];
    if (v == f || v == maxson[u]) continue;
    dfs2(v, u, v);
  }
}
void build(int a, int l, int r) {
  t[a].l = l;
  t[a].r = r;
  t[a].tag = false;
  if (l == r) {
    t[a].data = tmp[link[l]];
    return;
  }
  int mid = (l + r) >> 1;
  build(a << 1, l, mid);
  build(a << 1 | 1, mid + 1, r);
  t[a].data = max(t[a << 1].data, t[a << 1 | 1].data);
}
void pushdown(int a) {
  int l = a << 1, r = a << 1 | 1;
  t[a].tag = false;
  t[l].data = min(t[l].data, t[a].data);
  t[r].data = min(t[r].data, t[a].data);
  t[l].tag = t[r].tag = true;
}
void update(int a, int l, int r, int data) {
  if (t[a].l >= l && t[a].r <= r) {
    t[a].data = min(t[a].data, data);
    t[a].tag = true;
    return;
  }
  if (t[a].tag) pushdown(a);
  int mid = (t[a].l + t[a].r) >> 1;
  if (l <= mid) update(a << 1, l, r, data);
  if (r > mid) update(a << 1 | 1, l, r, data);
}
int querymax(int a, int l, int r) {
  if (t[a].l >= l && t[a].r <= r) return t[a].data;
  if (t[a].tag) pushdown(a);
  int mid = (t[a].l + t[a].r) >> 1, res = 0;
  if (l <= mid) res = max(res, querymax(a << 1, l, r));
  if (r > mid) res = max(res, querymax(a << 1 | 1, l, r));
  return res;
}
int querymin(int a, int l, int r) {
  if (t[a].l >= l && t[a].r <= r) return t[a].data;
  if (t[a].tag) pushdown(a);
  int mid = (t[a].l + t[a].r) >> 1, res = INF;
  if (l <= mid) res = min(res, querymin(a << 1, l, r));
  if (r > mid) res = min(res, querymin(a << 1 | 1, l, r));
  return res;
}
int solve(int u, int v) {
  int res = 0;
  while (belong[u] != belong[v]) {
    if (d[belong[u]] < d[belong[v]]) swap(u, v);
    res = max(res, querymax(1, id[belong[u]], id[u]));
    u = fa[belong[u]];
  }
  if (u != v) {
    if (d[u] > d[v]) swap(u, v);
    res = max(res, querymax(1, id[u] + 1, id[v]));
  }
  return res - 1;
}
void fix(int u, int v, int w) {
  while (belong[u] != belong[v]) {
    if (d[belong[u]] < d[belong[v]]) swap(u, v);
    update(1, id[belong[u]], id[u], w);
    u = fa[belong[u]];
  }
  if (u != v) {
    if (d[u] > d[v]) swap(u, v);
    update(1, id[u] + 1, id[v], w);
  }
}
int solve2(int u, int v) {
  int res = INF;
  while (belong[u] != belong[v]) {
    if (d[belong[u]] < d[belong[v]]) swap(u, v);
    res = min(res, querymin(1, id[belong[u]], id[u]));
    u = fa[belong[u]];
  }
  if (u != v) {
    if (d[u] > d[v]) swap(u, v);
    res = min(res, querymin(1, id[u] + 1, id[v]));
  }
  if (res == INF) res = 0;
  return res - 1;
}
int work() {
  n = read();
  m = read();
  for (int i = 1; i <= n; i++) f[i] = i;
  for (int i = 1; i <= m; i++) {
    e[i].from = read();
    e[i].to = read();
    e[i].dis = read();
    e[i].id = i;
  }
  sort(e + 1, e + m + 1);
  for (int i = 1; i <= m; i++) {
    int u = e[i].from, v = e[i].to, w = e[i].dis;
    int a = ffind(u), b = ffind(v);
    if (a != b) {
      f[a] = b;
      add(u, v, w);
      add(v, u, w);
    } else
      flag[i] = true;
  }
  dfs1(1, 0);
  dfs2(1, 0, 1);
  build(1, 1, n);
  for (int i = 1; i <= m; i++) {
    if (!flag[i]) continue;
    ans[e[i].id] = solve(e[i].from, e[i].to);
  }
  memset(tmp, INF, sizeof(tmp));
  build(1, 1, n);
  for (int i = 1; i <= m; i++) {
    if (!flag[i]) continue;
    fix(e[i].from, e[i].to, e[i].dis);
  }
  for (int i = 1; i <= m; i++) {
    if (flag[i]) continue;
    ans[e[i].id] = solve2(e[i].from, e[i].to);
  }
  for (int i = 1; i <= m; i++) printf("%d ", ans[i]);
  return 0;
}
}  // namespace Dango
int main() { return Dango::work(); }

```