#include <bits/stdc++.h>
using namespace std;
struct Segment {
  int coverTime, coverSize, size;
  Segment() {}
  Segment(int coverTime, int coverSize, int size)
      : coverTime(coverTime), coverSize(coverSize), size(size) {}
  Segment operator+(const Segment &rhs) const {
    return Segment(0, coverSize + rhs.coverSize, size + rhs.size);
  }
};
const int MAXN = 100000;
const int MAXNODE = MAXN << 2;
struct SegmentTree {
  int n;
  Segment seg[MAXNODE];
  static int LEFT(int idx) { return idx << 1; }
  static int RIGHT(int idx) { return (idx << 1) | 1; }
  void _build(int idx, int lower, int upper) {
    seg[idx] = Segment(0, 0, upper - lower + 1);
    if (lower == upper) return;
    int middle = (lower + upper) >> 1;
    _build(LEFT(idx), lower, middle);
    _build(RIGHT(idx), middle + 1, upper);
  }
  void init(int n) {
    this->n = n;
    _build(1, 0, n - 1);
  }
  int l, r, v;
  void _modify(int idx, int lower, int upper) {
    if (l <= lower && upper <= r) {
      if (!seg[idx].coverTime) {
        seg[idx].coverSize = seg[idx].size;
      }
      seg[idx].coverTime += v;
      if (!seg[idx].coverTime) {
        seg[idx] = lower == upper ? Segment(0, 0, 1)
                                  : seg[LEFT(idx)] + seg[RIGHT(idx)];
      }
      return;
    }
    int middle = (lower + upper) >> 1;
    if (r <= middle) {
      _modify(LEFT(idx), lower, middle);
    } else if (middle < l) {
      _modify(RIGHT(idx), middle + 1, upper);
    } else {
      _modify(LEFT(idx), lower, middle);
      _modify(RIGHT(idx), middle + 1, upper);
    }
    if (!seg[idx].coverTime) {
      seg[idx] = seg[LEFT(idx)] + seg[RIGHT(idx)];
    }
  }
  void modify(int l, int r, int v) {
    this->l = l;
    this->r = r;
    this->v = v;
    _modify(1, 0, n - 1);
  }
  int calc() { return seg[1].coverSize; }
};
int n, m, a[MAXN], b[MAXN], order[MAXN], in[MAXN], out[MAXN], stamp,
    answer[MAXN];
vector<int> adj[MAXN], cover[MAXN];
SegmentTree sgt;
void dfsOrder(int u, int parent) {
  in[u] = stamp;
  order[stamp++] = u;
  for (typeof((adj[u]).begin()) it = (adj[u]).begin(); it != (adj[u]).end();
       it++) {
    int v = *it;
    if (parent == v) continue;
    dfsOrder(v, u);
  }
  out[u] = stamp - 1;
}
void dfs(int u, int parent) {
  for (typeof((cover[u]).begin()) it = (cover[u]).begin();
       it != (cover[u]).end(); it++) {
    int x = a[*it], y = b[*it];
    sgt.modify(in[x], out[x], 1);
    sgt.modify(in[y], out[y], 1);
  }
  answer[u] = sgt.calc();
  for (typeof((adj[u]).begin()) it = (adj[u]).begin(); it != (adj[u]).end();
       it++) {
    int v = *it;
    if (parent == v) continue;
    dfs(v, u);
  }
  for (typeof((cover[u]).begin()) it = (cover[u]).begin();
       it != (cover[u]).end(); it++) {
    int x = a[*it], y = b[*it];
    sgt.modify(in[x], out[x], -1);
    sgt.modify(in[y], out[y], -1);
  }
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = (1); i < (n); i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    u--;
    v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  for (int i = (0); i < (m); i++) {
    scanf("%d%d", &a[i], &b[i]);
    a[i]--;
    b[i]--;
    cover[a[i]].push_back(i);
    cover[b[i]].push_back(i);
  }
  stamp = 0;
  dfsOrder(0, -1);
  sgt.init(n);
  dfs(0, -1);
  for (int i = (0); i < (n); i++) {
    printf("%d ", answer[i] ? answer[i] - 1 : 0);
  }
  putchar('\n');
  return 0;
}

### Prompt

Generate a cpp solution to the following problem:

The Little Elephant loves trees very much, he especially loves root trees.

He's got a tree consisting of n nodes (the nodes are numbered from 1 to n), with root at node number 1. Each node of the tree contains some list of numbers which initially is empty. 

The Little Elephant wants to apply m operations. On the i-th operation (1 ≤ i ≤ m) he first adds number i to lists of all nodes of a subtree with the root in node number ai, and then he adds number i to lists of all nodes of the subtree with root in node bi.

After applying all operations the Little Elephant wants to count for each node i number ci — the number of integers j (1 ≤ j ≤ n; j ≠ i), such that the lists of the i-th and the j-th nodes contain at least one common number.

Help the Little Elephant, count numbers ci for him.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 105) — the number of the tree nodes and the number of operations. 

Each of the following n - 1 lines contains two space-separated integers, ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi), that mean that there is an edge between nodes number ui and vi. 

Each of the following m lines contains two space-separated integers, ai and bi (1 ≤ ai, bi ≤ n, ai ≠ bi), that stand for the indexes of the nodes in the i-th operation.

It is guaranteed that the given graph is an undirected tree.

Output

In a single line print n space-separated integers — c1, c2, ..., cn.

Examples

Input

5 1
1 2
1 3
3 5
3 4
2 3


Output

0 3 3 3 3 

Input

11 3
1 2
2 3
2 4
1 5
5 6
5 7
5 8
6 9
8 10
8 11
2 9
3 6
2 8


Output

0 6 7 6 0 2 0 5 4 5 5 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct Segment {
  int coverTime, coverSize, size;
  Segment() {}
  Segment(int coverTime, int coverSize, int size)
      : coverTime(coverTime), coverSize(coverSize), size(size) {}
  Segment operator+(const Segment &rhs) const {
    return Segment(0, coverSize + rhs.coverSize, size + rhs.size);
  }
};
const int MAXN = 100000;
const int MAXNODE = MAXN << 2;
struct SegmentTree {
  int n;
  Segment seg[MAXNODE];
  static int LEFT(int idx) { return idx << 1; }
  static int RIGHT(int idx) { return (idx << 1) | 1; }
  void _build(int idx, int lower, int upper) {
    seg[idx] = Segment(0, 0, upper - lower + 1);
    if (lower == upper) return;
    int middle = (lower + upper) >> 1;
    _build(LEFT(idx), lower, middle);
    _build(RIGHT(idx), middle + 1, upper);
  }
  void init(int n) {
    this->n = n;
    _build(1, 0, n - 1);
  }
  int l, r, v;
  void _modify(int idx, int lower, int upper) {
    if (l <= lower && upper <= r) {
      if (!seg[idx].coverTime) {
        seg[idx].coverSize = seg[idx].size;
      }
      seg[idx].coverTime += v;
      if (!seg[idx].coverTime) {
        seg[idx] = lower == upper ? Segment(0, 0, 1)
                                  : seg[LEFT(idx)] + seg[RIGHT(idx)];
      }
      return;
    }
    int middle = (lower + upper) >> 1;
    if (r <= middle) {
      _modify(LEFT(idx), lower, middle);
    } else if (middle < l) {
      _modify(RIGHT(idx), middle + 1, upper);
    } else {
      _modify(LEFT(idx), lower, middle);
      _modify(RIGHT(idx), middle + 1, upper);
    }
    if (!seg[idx].coverTime) {
      seg[idx] = seg[LEFT(idx)] + seg[RIGHT(idx)];
    }
  }
  void modify(int l, int r, int v) {
    this->l = l;
    this->r = r;
    this->v = v;
    _modify(1, 0, n - 1);
  }
  int calc() { return seg[1].coverSize; }
};
int n, m, a[MAXN], b[MAXN], order[MAXN], in[MAXN], out[MAXN], stamp,
    answer[MAXN];
vector<int> adj[MAXN], cover[MAXN];
SegmentTree sgt;
void dfsOrder(int u, int parent) {
  in[u] = stamp;
  order[stamp++] = u;
  for (typeof((adj[u]).begin()) it = (adj[u]).begin(); it != (adj[u]).end();
       it++) {
    int v = *it;
    if (parent == v) continue;
    dfsOrder(v, u);
  }
  out[u] = stamp - 1;
}
void dfs(int u, int parent) {
  for (typeof((cover[u]).begin()) it = (cover[u]).begin();
       it != (cover[u]).end(); it++) {
    int x = a[*it], y = b[*it];
    sgt.modify(in[x], out[x], 1);
    sgt.modify(in[y], out[y], 1);
  }
  answer[u] = sgt.calc();
  for (typeof((adj[u]).begin()) it = (adj[u]).begin(); it != (adj[u]).end();
       it++) {
    int v = *it;
    if (parent == v) continue;
    dfs(v, u);
  }
  for (typeof((cover[u]).begin()) it = (cover[u]).begin();
       it != (cover[u]).end(); it++) {
    int x = a[*it], y = b[*it];
    sgt.modify(in[x], out[x], -1);
    sgt.modify(in[y], out[y], -1);
  }
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = (1); i < (n); i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    u--;
    v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  for (int i = (0); i < (m); i++) {
    scanf("%d%d", &a[i], &b[i]);
    a[i]--;
    b[i]--;
    cover[a[i]].push_back(i);
    cover[b[i]].push_back(i);
  }
  stamp = 0;
  dfsOrder(0, -1);
  sgt.init(n);
  dfs(0, -1);
  for (int i = (0); i < (n); i++) {
    printf("%d ", answer[i] ? answer[i] - 1 : 0);
  }
  putchar('\n');
  return 0;
}

```