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 
#include <bits/stdc++.h>
using namespace std;
namespace IO {
const int MAXIOSIZE = 1 << 24 | 1;
unsigned char buf[MAXIOSIZE], *p1, *p2;
template <typename T>
void read(T& x) {
  x = 0;
  char ch =
      (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 24, stdin), p1 == p2)
           ? EOF
           : *p1++);
  bool flg = false;
  for (; ch < '0' || '9' < ch;
       ch = (p1 == p2 &&
                     (p2 = (p1 = buf) + fread(buf, 1, 1 << 24, stdin), p1 == p2)
                 ? EOF
                 : *p1++))
    if (ch == '-') flg |= true;
  for (; '0' <= ch && ch <= '9';
       ch = (p1 == p2 &&
                     (p2 = (p1 = buf) + fread(buf, 1, 1 << 24, stdin), p1 == p2)
                 ? EOF
                 : *p1++))
    x = x * 10 + ch - '0';
  flg ? x = -x : 0;
}
template <typename T>
void out(const T& x) {
  if (x > 9) out(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
inline void write(const T& x, const char& ed = ' ') {
  if (x < 0)
    putchar('-'), out(-x);
  else
    out(x);
  putchar(ed);
}
}  // namespace IO
const int MAXN = 1e5 + 10;
int n, m;
vector<int> E[MAXN], opt[MAXN];
struct Persistent_Segment_Tree {
  struct Node {
    int mnval, mncnt, tag;
  } t[MAXN << 2];
  void pushup(int k) {
    t[k].mnval = min(t[k << 1].mnval, t[k << 1 | 1].mnval);
    t[k].mncnt = (t[k].mnval == t[k << 1].mnval) * t[k << 1].mncnt +
                 (t[k].mnval == t[k << 1 | 1].mnval) * t[k << 1 | 1].mncnt;
  }
  void build(int k, int l, int r) {
    if (l == r) return t[k].mnval = 0, t[k].mncnt = 1, void();
    build(k << 1, l, ((l + r) >> 1)), build(k << 1 | 1, ((l + r) >> 1) + 1, r);
    pushup(k);
  }
  void pushdown(int k) {
    t[k << 1].tag += t[k].tag, t[k << 1 | 1].tag += t[k].tag;
    t[k << 1].mnval += t[k].tag, t[k << 1 | 1].mnval += t[k].tag;
    t[k].tag = 0;
  }
  void modify(int k, int l, int r, int ql, int qr, int val) {
    if (ql <= l && r <= qr) return t[k].tag += val, t[k].mnval += val, void();
    pushdown(k);
    if (ql <= ((l + r) >> 1)) modify(k << 1, l, ((l + r) >> 1), ql, qr, val);
    if (qr > ((l + r) >> 1))
      modify(k << 1 | 1, ((l + r) >> 1) + 1, r, ql, qr, val);
    pushup(k);
  }
} sgt;
int dfn[MAXN], sz[MAXN], dfsclock;
void dfs(int u, int fr) {
  dfn[u] = ++dfsclock, sz[u] = 1;
  for (int v : E[u]) {
    if (v == fr) continue;
    dfs(v, u);
    sz[u] += sz[v];
  }
}
int ans[MAXN];
int cov;
void calc(int u, int fr) {
  if (opt[u].size()) sgt.modify(1, 1, n, dfn[u], dfn[u] + sz[u] - 1, 1), cov++;
  for (int v : opt[u]) sgt.modify(1, 1, n, dfn[v], dfn[v] + sz[v] - 1, 1);
  if (sgt.t[1].mnval > 0)
    ans[u] = n - (cov > 0);
  else
    ans[u] = n - sgt.t[1].mncnt - (cov > 0);
  for (int v : E[u]) {
    if (v == fr) continue;
    calc(v, u);
  }
  if (opt[u].size()) sgt.modify(1, 1, n, dfn[u], dfn[u] + sz[u] - 1, -1), cov--;
  for (int v : opt[u]) sgt.modify(1, 1, n, dfn[v], dfn[v] + sz[v] - 1, -1);
}
int main() {
  IO::read(n), IO::read(m);
  for (int i = (1), iend = (n - 1); i <= iend; ++i) {
    int u, v;
    IO::read(u), IO::read(v);
    E[u].push_back(v), E[v].push_back(u);
  }
  dfs(1, 0);
  sgt.build(1, 1, n);
  for (int i = (1), iend = (m); i <= iend; ++i) {
    int u, v;
    IO::read(u), IO::read(v);
    opt[u].push_back(v), opt[v].push_back(u);
  }
  calc(1, 0);
  for (int i = (1), iend = (n); i <= iend; ++i) {
    IO::write(ans[i]);
  }
  return 0;
}
