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 maxn = 2e5 + 1;
const int inf = 0x3f3f3f3f;
int n, m;
struct Edge {
  int u, v, w, id;
  Edge(int pu = 0, int pv = 0, int pw = 0, int pid = 0) {
    u = pu;
    v = pv;
    w = pw;
    id = pid;
  }
  int nb(int i) { return u + v - i; }
  bool operator<(Edge b) const {
    if (w > b.w)
      return 1;
    else
      return w == b.w && id < b.id;
  }
};
struct comp1 {
  bool operator()(const Edge a, const Edge b) { return a.w > b.w; }
};
Edge e[maxn];
int sfa[maxn];
set<Edge> mst;
set<Edge> nmst;
set<Edge>::iterator ite;
vector<Edge> g[maxn];
int findset(int a) {
  if (!sfa[a])
    return a;
  else
    return sfa[a] = findset(sfa[a]);
}
int unionset(int a, int b) {
  a = findset(a);
  b = findset(b);
  sfa[b] = a;
  return a;
}
priority_queue<Edge, vector<Edge>, comp1> pq;
void kruskal() {
  for (int i = 1; i <= m; i++) pq.push(e[i]);
  memset(sfa, 0, sizeof sfa);
  while (pq.size()) {
    Edge te = pq.top();
    pq.pop();
    if (findset(te.u) != findset(te.v)) {
      unionset(te.u, te.v);
      mst.insert(te);
      g[te.u].push_back(te);
      g[te.v].push_back(te);
    } else
      nmst.insert(te);
  }
}
int dep[maxn];
int son[maxn];
int top[maxn];
int sz[maxn];
int efather[maxn];
int echild[maxn];
int w[maxn];
int nw, nseq;
int seq[maxn];
bool vis[maxn];
void dfs1(int u) {
  vis[u] = true;
  sz[u] = 1;
  for (int i = 0; i < g[u].size(); i++) {
    Edge &te = g[u][i];
    int v = te.nb(u);
    if (vis[v]) continue;
    dep[v] = dep[u] + 1;
    efather[v] = te.id;
    echild[te.id] = v;
    dfs1(v);
    sz[u] += sz[v];
    if (sz[v] > sz[son[u]]) son[u] = v;
  }
}
void dfs1() {
  memset(son, 0, sizeof son);
  memset(vis, 0, sizeof vis);
  dep[1] = 1;
  efather[1] = 0;
  sz[0] = 0;
  dfs1(1);
}
void dfs2(int u) {
  if (son[u]) {
    w[son[u]] = nw;
    seq[nw++] = son[u];
    top[son[u]] = top[u];
    dfs2(son[u]);
  }
  for (int i = 0; i < g[u].size(); i++) {
    Edge &te = g[u][i];
    int v = te.nb(u);
    if (efather[u] == te.id || v == son[u]) continue;
    w[v] = nw;
    seq[nw++] = v;
    top[v] = v;
    dfs2(v);
  }
}
void dfs2() {
  nw = 1;
  top[1] = 1;
  w[1] = 0;
  seq[0] = 1;
  dfs2(1);
}
int v1flag[(1 << 19) - 2];
int v1[(1 << 19) - 2];
int v2[(1 << 19) - 2];
void buildv2(int l, int r, int i) {
  if (l == r) {
    v2[i] = e[efather[seq[l]]].w;
    return;
  }
  int mid = (l + r) / 2;
  int li = 2 * i + 1, ri = 2 * i + 2;
  buildv2(l, mid, li);
  buildv2(mid + 1, r, ri);
  v2[i] = max(v2[li], v2[ri]);
}
void build() {
  memset(v1flag, 0x3f, sizeof v1flag);
  memset(v1, 0x3f, sizeof v1);
  buildv2(1, nw - 1, 0);
}
void pushdownv1(int i) {
  if (v1flag[i] != inf) {
    int li = 2 * i + 1, ri = 2 * i + 2;
    v1flag[li] = v1[li] = v1flag[ri] = v1[ri] = v1flag[i];
    v1flag[i] = inf;
  }
}
void stsetv1(int l, int r, int i, int a, int b, int key) {
  if (a <= l && b >= r) {
    v1flag[i] = key;
    v1[i] = key;
    return;
  }
  int mid = (l + r) / 2;
  int li = 2 * i + 1, ri = 2 * i + 2;
  pushdownv1(i);
  if (a <= mid) stsetv1(l, mid, li, a, b, key);
  if (b > mid) stsetv1(mid + 1, r, ri, a, b, key);
  v1[i] = min(v1[li], v1[ri]);
}
int stqueryv1(int l, int r, int i, int p) {
  if (l == r && l == p) {
    return v1[i];
  }
  int mid = (l + r) / 2;
  int li = 2 * i + 1, ri = 2 * i + 2;
  pushdownv1(i);
  if (p <= mid)
    return stqueryv1(l, mid, li, p);
  else
    return stqueryv1(mid + 1, r, ri, p);
}
int stqueryv2(int l, int r, int i, int a, int b) {
  if (a <= l && b >= r) return v2[i];
  int mid = (l + r) / 2;
  int li = 2 * i + 1, ri = 2 * i + 2;
  int res = -1;
  if (a <= mid) res = max(res, stqueryv2(l, mid, li, a, b));
  if (b > mid) res = max(res, stqueryv2(mid + 1, r, ri, a, b));
  return res;
}
void setv1(int u, int v, int key) {
  while (top[u] != top[v]) {
    if (dep[top[u]] > dep[top[v]]) {
      stsetv1(1, nw - 1, 0, w[top[u]], w[u], key);
      u = e[efather[top[u]]].nb(top[u]);
    } else {
      stsetv1(1, nw - 1, 0, w[top[v]], w[v], key);
      v = e[efather[top[v]]].nb(top[v]);
    }
  }
  if (dep[u] == dep[v]) return;
  if (dep[u] < dep[v]) {
    stsetv1(1, nw - 1, 0, w[u] + 1, w[v], key);
  } else {
    stsetv1(1, nw - 1, 0, w[v] + 1, w[u], key);
  }
}
int queryv2(int u, int v) {
  int res = -1;
  while (top[u] != top[v]) {
    if (dep[top[u]] > dep[top[v]]) {
      res = max(res, stqueryv2(1, nw - 1, 0, w[top[u]], w[u]));
      u = e[efather[top[u]]].nb(top[u]);
    } else {
      res = max(res, stqueryv2(1, nw - 1, 0, w[top[v]], w[v]));
      v = e[efather[top[v]]].nb(top[v]);
    }
  }
  if (dep[u] == dep[v]) return res;
  if (dep[u] < dep[v])
    res = max(res, stqueryv2(1, nw - 1, 0, w[u] + 1, w[v]));
  else
    res = max(res, stqueryv2(1, nw - 1, 0, w[v] + 1, w[u]));
  return res;
}
int res[maxn];
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;
  }
  kruskal();
  dfs1();
  dfs2();
  build();
  memset(res, 0x3f, sizeof res);
  for (ite = nmst.begin(); ite != nmst.end(); ite++) {
    res[ite->id] = queryv2(ite->u, ite->v) - 1;
    setv1(ite->u, ite->v, ite->w - 1);
  }
  for (ite = mst.begin(); ite != mst.end(); ite++) {
    res[ite->id] = stqueryv1(1, nw - 1, 0, w[echild[ite->id]]);
  }
  for (int i = 1; i <= m; i++) printf("%d ", res[i] == inf ? -1 : res[i]);
  puts("");
}
