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 
#include <bits/stdc++.h>
using namespace std;
const int N = 200001;
const int INF = 1061109567;
int n, m;
struct Edge {
  int to, val, id, next;
} edge[N << 1];
int head[N], cnt;
void add_edge(int u, int v, int w, int id) {
  cnt++;
  edge[cnt].to = v;
  edge[cnt].val = w;
  edge[cnt].id = id;
  edge[cnt].next = head[u];
  head[u] = cnt;
  return;
}
struct Line {
  int u, v, w;
  int id;
  bool flag;
} e[N << 1];
bool cmp(Line x, Line y) { return x.w < y.w; }
struct Node {
  int l, r;
  int Max, Min, lazy;
} tree[N << 2];
int pre[N], a[N], w[N];
int ans[N];
int f[N];
int getf(int v) {
  if (v == f[v]) return v;
  f[v] = getf(f[v]);
  return f[v];
}
bool merge(int u, int v) {
  int f1 = getf(u), f2 = getf(v);
  if (f1 != f2) {
    f[f2] = f1;
    return true;
  }
  return false;
}
void kruskal() {
  for (int i = 1; i <= n; i++) f[i] = i;
  for (int i = 1; i <= m; i++)
    if (merge(e[i].u, e[i].v)) {
      e[i].flag = true;
      add_edge(e[i].u, e[i].v, e[i].w, e[i].id);
      add_edge(e[i].v, e[i].u, e[i].w, e[i].id);
    }
  return;
}
int fa[N], dep[N], size[N], son[N];
void dfs1(int u, int father) {
  size[u] = 1;
  fa[u] = father;
  dep[u] = dep[father] + 1;
  for (int i = head[u]; i; i = edge[i].next) {
    int v = edge[i].to;
    if (v == father) continue;
    pre[v] = edge[i].id;
    a[v] = edge[i].val;
    dfs1(v, u);
    size[u] += size[v];
    if (size[v] > size[son[u]]) son[u] = v;
  }
  return;
}
int top[N], dfn[N], Index;
void dfs2(int u, int father) {
  dfn[u] = ++Index;
  top[u] = father;
  w[Index] = a[u];
  if (!son[u]) return;
  dfs2(son[u], father);
  for (int i = head[u]; i; i = edge[i].next) {
    int v = edge[i].to;
    if (v == son[u] || v == fa[u]) continue;
    dfs2(v, v);
  }
  return;
}
void push_up(int i) {
  tree[i].Max = max(tree[i * 2].Max, tree[i * 2 + 1].Max);
  tree[i].Min = min(tree[i * 2].Min, tree[i * 2 + 1].Min);
  return;
}
void push_down(int i) {
  if (tree[i].lazy >= INF) return;
  tree[i * 2].Min = min(tree[i * 2].Min, tree[i].lazy);
  tree[i * 2].lazy = min(tree[i * 2].lazy, tree[i].lazy);
  tree[i * 2 + 1].Min = min(tree[i * 2 + 1].Min, tree[i].lazy);
  tree[i * 2 + 1].lazy = min(tree[i * 2 + 1].lazy, tree[i].lazy);
  tree[i].lazy = INF;
  return;
}
void build(int i, int l, int r) {
  tree[i].l = l, tree[i].r = r;
  tree[i].Min = tree[i].lazy = INF;
  if (l == r) {
    tree[i].Max = w[l];
    return;
  }
  int mid = (l + r) / 2;
  build(i * 2, l, mid);
  build(i * 2 + 1, mid + 1, r);
  push_up(i);
  return;
}
void update(int i, int l, int r, int val) {
  if (r < tree[i].l || l > tree[i].r) return;
  if (l <= tree[i].l && tree[i].r <= r) {
    tree[i].Min = min(tree[i].Min, val);
    tree[i].lazy = min(tree[i].lazy, val);
    return;
  }
  push_down(i);
  if (l <= tree[i * 2].r) update(i * 2, l, r, val);
  if (r >= tree[i * 2 + 1].l) update(i * 2 + 1, l, r, val);
  push_up(i);
  return;
}
int querymax(int i, int l, int r) {
  if (r < tree[i].l || l > tree[i].r) return 0;
  if (l <= tree[i].l && tree[i].r <= r) return tree[i].Max;
  push_down(i);
  int res = 0;
  if (l <= tree[i * 2].r) res = max(res, querymax(i * 2, l, r));
  if (r >= tree[i * 2 + 1].l) res = max(res, querymax(i * 2 + 1, l, r));
  return res;
}
int querymin(int i, int u) {
  if (tree[i].l == tree[i].r) return tree[i].Min;
  push_down(i);
  if (u <= tree[i * 2].r)
    return querymin(i * 2, u);
  else
    return querymin(i * 2 + 1, u);
}
int getmax(int u, int v) {
  int res = 0;
  if (dep[u] < dep[v]) swap(u, v);
  while (top[u] != top[v]) {
    if (dep[top[u]] < dep[top[v]]) swap(u, v);
    res = max(res, querymax(1, dfn[top[u]], dfn[u]));
    u = fa[top[u]];
  }
  if (dep[u] > dep[v]) swap(u, v);
  res = max(res, querymax(1, dfn[u] + 1, dfn[v]));
  return res;
}
void modifymin(int u, int v, int val) {
  if (dep[u] < dep[v]) swap(u, v);
  while (top[u] != top[v]) {
    if (dep[top[u]] < dep[top[v]]) swap(u, v);
    update(1, dfn[top[u]], dfn[u], val);
    u = fa[top[u]];
  }
  if (dep[u] > dep[v]) swap(u, v);
  update(1, dfn[u] + 1, dfn[v], val);
  return;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    scanf("%d%d%d", &e[i].u, &e[i].v, &e[i].w);
    e[i].id = i;
  }
  sort(e + 1, e + m + 1, cmp);
  kruskal();
  dfs1(1, 0);
  dfs2(1, 1);
  build(1, 1, n);
  for (int i = 1; i <= m; i++)
    if (!e[i].flag) {
      ans[e[i].id] = getmax(e[i].u, e[i].v) - 1;
      modifymin(e[i].u, e[i].v, e[i].w);
    }
  for (int i = 2; i <= n; i++) {
    int res = querymin(1, dfn[i]);
    if (res >= INF)
      ans[pre[i]] = -1;
    else
      ans[pre[i]] = res - 1;
  }
  for (int i = 1; i <= m; i++) printf("%d ", ans[i]);
  return 0;
}
