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 = 2e5 + 5;
const int INF = 2e9;
struct Node {
  int U, V, W, idx;
  bool operator<(Node other) const { return W < other.W; }
};
int n, m, timer = 0;
int parent[N], level[N];
vector<pair<int, int> > edge[N];
int sz[N], tin[N], tout[N], nxt[N];
int up[N][25], val[N][25];
int ST[4 * N], lazy[4 * N];
int ans[N];
vector<Node> all, e1, e2;
int find_set(int u) {
  if (u == parent[u]) return u;
  return parent[u] = find_set(parent[u]);
}
bool union_set(int u, int v) {
  u = find_set(u);
  v = find_set(v);
  if (u == v) return false;
  if (level[u] < level[v]) swap(u, v);
  parent[v] = u;
  if (level[u] == level[v]) ++level[u];
  return true;
}
void getSize(int u) {
  sz[u] = 1;
  for (auto &adj : edge[u]) {
    int v = adj.second;
    if (v == parent[u]) swap(adj, edge[u].back());
    v = adj.second;
    if (v == parent[u]) continue;
    parent[v] = u;
    getSize(v);
    sz[u] += sz[v];
    if (sz[v] > sz[edge[u][0].second]) {
      swap(adj, edge[u][0]);
    }
  }
  if (edge[u].back().second == parent[u]) edge[u].pop_back();
}
void getEuler(int u, int w) {
  up[u][0] = parent[u];
  for (int j = 1; j <= 20; ++j) up[u][j] = up[up[u][j - 1]][j - 1];
  val[u][0] = w;
  for (int j = 1; j <= 20; ++j)
    val[u][j] = max(val[u][j - 1], val[up[u][j - 1]][j - 1]);
  tin[u] = ++timer;
  for (pair<int, int> adj : edge[u]) {
    int v = adj.second;
    int w = adj.first;
    nxt[v] = (v == edge[u][0].second ? nxt[u] : v);
    getEuler(v, w);
  }
  tout[u] = timer;
}
bool ancestor(int u, int v) { return tin[u] <= tin[v] && tout[v] <= tout[u]; }
int lca(int u, int v) {
  if (ancestor(u, v)) return u;
  if (ancestor(v, u)) return v;
  for (int j = 20; j >= 0; --j) {
    if (!ancestor(up[u][j], v)) {
      u = up[u][j];
    }
  }
  return up[u][0];
}
int getVal(int u, int v) {
  if (u == v) return 0;
  int res = 0;
  for (int j = 20; j >= 0; --j) {
    if (!ancestor(up[u][j], v)) {
      res = max(res, val[u][j]);
      u = up[u][j];
    }
  }
  return max(res, val[u][0]);
}
int getNode(int u, int v) {
  for (int j = 20; j >= 0; --j)
    if (!ancestor(up[u][j], v)) u = up[u][j];
  return u;
}
void push(int node, int seg_l, int seg_r) {
  if (lazy[node] == INF) return;
  if (seg_l != seg_r) {
    lazy[node << 1] = min(lazy[node << 1], lazy[node]);
    lazy[node << 1 | 1] = min(lazy[node << 1 | 1], lazy[node]);
    ST[node << 1] = min(ST[node << 1], lazy[node << 1]);
    ST[node << 1 | 1] = min(ST[node << 1 | 1], lazy[node << 1 | 1]);
  }
  lazy[node] = INF;
}
void update(int node, int seg_l, int seg_r, int l, int r, int cur) {
  push(node, seg_l, seg_r);
  if (r < seg_l || l > seg_r) {
    return;
  }
  if (l <= seg_l && seg_r <= r) {
    lazy[node] = cur;
    ST[node] = min(ST[node], cur);
    push(node, seg_l, seg_r);
  } else {
    int seg_mid = (seg_l + seg_r) >> 1;
    update(node << 1, seg_l, seg_mid, l, r, cur);
    update(node << 1 | 1, seg_mid + 1, seg_r, l, r, cur);
    ST[node] = min(ST[node << 1], ST[node << 1 | 1]);
  }
}
int get(int node, int seg_l, int seg_r, int pos) {
  push(node, seg_l, seg_r);
  if (pos < seg_l || pos > seg_r) {
    return INF;
  }
  if (seg_l == seg_r) {
    return ST[node];
  } else {
    int seg_mid = (seg_l + seg_r) >> 1;
    return min(get(node << 1, seg_l, seg_mid, pos),
               get(node << 1 | 1, seg_mid + 1, seg_r, pos));
  }
}
void updatePath(int u, int v, int w) {
  while (true) {
    if (nxt[u] == nxt[v]) {
      if (tin[u] > tin[v]) swap(u, v);
      update(1, 1, n, tin[u], tin[v], w);
      break;
    } else {
      if (tin[nxt[u]] < tin[nxt[v]]) swap(u, v);
      update(1, 1, n, tin[nxt[u]], tin[u], w);
      u = parent[nxt[u]];
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int i = 1; i <= m; ++i) {
    int u, v, w;
    cin >> u >> v >> w;
    all.push_back({u, v, w, i});
  }
  sort(all.begin(), all.end());
  for (int i = 1; i <= n; ++i) parent[i] = i;
  for (auto e : all) {
    int u = e.U;
    int v = e.V;
    int w = e.W;
    if (union_set(u, v)) {
      edge[u].push_back({w, v});
      edge[v].push_back({w, u});
      e1.push_back(e);
    } else {
      e2.push_back(e);
    }
  }
  for (int i = 1; i <= n; ++i) parent[i] = 0;
  for (int i = 1; i <= 4 * n; ++i) {
    ST[i] = lazy[i] = INF;
  }
  getSize(1);
  getEuler(1, 0);
  tout[0] = 1e9;
  for (auto e : e2) {
    int u = e.U;
    int v = e.V;
    int w = e.W;
    int root = lca(u, v);
    ans[e.idx] = max(getVal(u, root), getVal(v, root));
    int childU = getNode(u, root);
    int childV = getNode(v, root);
    if (childU != root) updatePath(u, childU, w);
    if (childV != root) updatePath(v, childV, w);
  }
  for (auto e : e1) {
    int u = e.U;
    int v = e.V;
    if (u != parent[v]) swap(u, v);
    ans[e.idx] = get(1, 1, n, tin[v]);
    if (ans[e.idx] == INF) ans[e.idx] = 0;
  }
  for (int i = 1; i <= m; ++i) cout << ans[i] - 1 << " ";
}
