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 inf = 1e9 + 1;
template <class T>
int getbit(T x, int pos) {
  return (x >> (pos - 1)) & 1;
}
template <class T>
void turn_on(T &x, int pos) {
  x = x | ((T)1 << (pos - 1));
}
template <class T>
void turn_off(T &x, int pos) {
  x = x & ~((T)1 << (pos - 1));
}
template <class T>
T sqr(T a) {
  return a * a;
}
struct edge {
  int u, v, w, id;
  bool selected;
  edge() { selected = false; }
} e[200002];
struct node {
  int val, lazy;
} st[200002 * 4];
int n, m, lab[200002], nChild[200002], l[200002], p[200002][20],
    chainHead[200002], nChain = 1;
int chainIn[200002], posInBase[200002], nBase, res[200002];
vector<pair<int, int> > a[200002];
int findset(int u) { return lab[u] <= 0 ? u : lab[u] = findset(lab[u]); }
void uni(int s, int t) {
  if (lab[s] < lab[t])
    lab[t] = s;
  else if (lab[s] > lab[t])
    lab[s] = t;
  else {
    lab[s] = t;
    lab[t]--;
  }
}
int buildTree(int u) {
  nChild[u] = 1;
  for (int i = 0; i < (int)a[u].size(); ++i) {
    int v = a[u][i].first;
    if (v == p[u][0]) continue;
    p[v][0] = u;
    nChild[u] += buildTree(v);
  }
  return nChild[u];
}
int level(int u) { return l[u] > 0 ? l[u] : l[u] = level(p[u][0]) + 1; }
bool cmp(edge a, edge b) { return a.w < b.w; }
void initHLD(int u) {
  if (chainHead[nChain] == 0) chainHead[nChain] = u;
  chainIn[u] = nChain;
  posInBase[u] = ++nBase;
  int hv = -1;
  for (int i = 0; i < (int)a[u].size(); ++i) {
    int v = a[u][i].first;
    if (v != p[u][0] && (hv == -1 || nChild[hv] < nChild[v])) hv = v;
  }
  if (hv != -1) initHLD(hv);
  for (int i = 0; i < (int)a[u].size(); ++i) {
    int v = a[u][i].first;
    if (v != p[u][0] && v != hv) {
      ++nChain;
      initHLD(v);
    }
  }
}
void down(int id, int type) {
  int tmp = st[id].lazy;
  st[id].lazy = inf;
  if (type == -1) st[id].lazy = 0;
  st[id * 2].lazy = abs(min(st[id * 2].lazy * type, tmp * type));
  st[id * 2].val = abs(min(st[id * 2].val * type, tmp * type));
  st[id * 2 + 1].lazy = abs(min(st[id * 2 + 1].lazy * type, tmp * type));
  st[id * 2 + 1].val = abs(min(st[id * 2 + 1].val * type, tmp * type));
}
void update(int u, int v, int newVal, int type, int l = 1, int r = n,
            int id = 1) {
  if (v < l || r < u) return;
  if (u <= l && r <= v) {
    st[id].val = abs(min(type * st[id].val, type * newVal));
    st[id].lazy = abs(min(type * st[id].lazy, type * newVal));
    return;
  }
  down(id, type);
  int mid = (l + r) / 2;
  update(u, v, newVal, type, l, mid, id * 2);
  update(u, v, newVal, type, mid + 1, r, id * 2 + 1);
  st[id].val = abs(min(type * st[id * 2].val, type * st[id * 2 + 1].val));
}
int get(int u, int v, int type, int l = 1, int r = n, int id = 1) {
  if (v < l || r < u) return type == 1 ? inf : 0;
  if (u <= l && r <= v) return st[id].val;
  down(id, type);
  int mid = (l + r) / 2;
  int res = abs(min(type * get(u, v, type, l, mid, id * 2),
                    type * get(u, v, type, mid + 1, r, id * 2 + 1)));
  st[id].val = abs(min(type * st[id * 2].val, type * st[id * 2 + 1].val));
  return res;
}
void update_hld(int u, int par, int newVal, int type) {
  if (chainIn[u] == chainIn[par]) {
    return update(posInBase[par] + 1, posInBase[u], newVal, type);
  }
  update(posInBase[chainHead[chainIn[u]]], posInBase[u], newVal, type);
  update_hld(p[chainHead[chainIn[u]]][0], par, newVal, type);
}
int get_hld(int u, int par, int type) {
  if (chainIn[u] == chainIn[par]) {
    return get(posInBase[par] + 1, posInBase[u], type);
  }
  return abs(
      min(get(posInBase[chainHead[chainIn[u]]], posInBase[u], type) * type,
          get_hld(p[chainHead[chainIn[u]]][0], par, type) * type));
}
int lca(int x, int y) {
  for (int k = 19; k >= 0; --k) {
    if (l[p[x][k]] >= l[y]) x = p[x][k];
  }
  for (int k = 19; k >= 0; --k) {
    if (l[p[y][k]] >= l[x]) y = p[y][k];
  }
  for (int k = 19; k >= 0; --k) {
    if (p[x][k] != p[y][k]) {
      x = p[x][k];
      y = p[y][k];
    }
  }
  while (x != y) {
    x = p[x][0];
    y = p[y][0];
  }
  return x;
}
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);
  for (int i = 1; i <= m; ++i) {
    int s = findset(e[i].u), t = findset(e[i].v);
    if (s != t) {
      uni(s, t);
      e[i].selected = true;
      a[e[i].u].push_back(pair<int, int>(e[i].v, e[i].w));
      a[e[i].v].push_back(pair<int, int>(e[i].u, e[i].w));
    }
  }
  buildTree(1);
  initHLD(1);
  l[1] = 1;
  for (int i = 1; i <= n; ++i) level(i);
  for (int i = 1; i <= 19; ++i)
    for (int j = 1; j <= n; ++j) p[j][i] = p[p[j][i - 1]][i - 1];
  for (int i = 1; i <= 4 * n; ++i) st[i].lazy = st[i].val = 0;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j < (int)a[i].size(); ++j) {
      int v = a[i][j].first;
      if (v == p[i][0]) update_hld(i, v, a[i][j].second, -1);
    }
  }
  for (int i = 1; i <= m; ++i) {
    if (!e[i].selected) {
      int u = e[i].u, v = e[i].v, x = lca(u, v);
      res[e[i].id] = max(get_hld(u, x, -1), get_hld(v, x, -1)) - 1;
    }
  }
  for (int i = 1; i <= 4 * n; ++i) st[i].val = st[i].lazy = inf;
  for (int i = 1; i <= m; ++i) {
    int u = e[i].u, v = e[i].v, x = lca(u, v);
    if (e[i].selected) continue;
    update_hld(u, x, e[i].w, 1);
    update_hld(v, x, e[i].w, 1);
  }
  for (int i = 1; i <= m; ++i) {
    if (!e[i].selected) continue;
    int u = e[i].u, v = e[i].v;
    if (u == p[v][0]) swap(u, v);
    int tmp = get_hld(u, v, 1);
    if (tmp == inf)
      res[e[i].id] = -1;
    else
      res[e[i].id] = tmp - 1;
  }
  for (int i = 1; i <= m; ++i) printf("%d ", res[i]);
}
