#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


int N, M;
char C[100'010];
vector<int> A, B;

vector<vector<int>> graph;


namespace brute {
vector<int> stack;
vector<Int> ans;
void dfs(int u, int p, int k) {
  if (C[u] == '{') {
    stack.push_back(0);
  } else if (C[u] == '|') {
    if (stack.empty()) return;
    ++stack.back();
  } else if (C[u] == '}') {
    if (stack.empty()) return;
    if (!~k) k = stack.back();
    if (k != stack.back()) return;
    stack.pop_back();
  } else {
    assert(false);
  }
  
  if (stack.empty()) {
    assert(~k);
    ++ans[k];
  }
  for (const int v : graph[u]) if (p != v) {
    dfs(v, u, k);
  }
  
  if (C[u] == '{') {
    stack.pop_back();
  } else if (C[u] == '|') {
    if (stack.empty()) assert(false);
    --stack.back();
  } else if (C[u] == '}') {
    assert(~k);
    stack.push_back(k);
  } else {
    assert(false);
  }
}

vector<Int> run() {
cerr<<"[brute::run]"<<endl;
  ans.assign(N, 0);
  for (int r = 0; r < N; ++r) {
    stack.clear();
    dfs(r, -1, -1);
  }
  return ans;
}
}  // brute


namespace sub2 {
vector<Int> run() {
cerr<<"[sub2::run]"<<endl;
  vector<Int> ans(N, 0);
  for (int phase = 0; phase < 2; ++phase) {
    vector<int> hei(N + 1, 0);
    vector<int> mate(N, -1);
    {
      vector<int> stack;
      for (int u = 0; u < N; ++u) {
        if (C[u] == '{') {
          hei[u + 1] = hei[u] + 1;
          stack.push_back(u);
        } else if (C[u] == '|') {
          hei[u + 1] = hei[u];
        } else if (C[u] == '}') {
          hei[u + 1] = hei[u] - 1;
          if (stack.size()) {
            const int v = stack.back();
            stack.pop_back();
            mate[v] = u;
            mate[u] = v;
          }
        }
      }
    }
    vector<pair<int, int>> ps;
    for (int u = 0; u < N; ++u) if (u < mate[u]) {
      ps.emplace_back(u, mate[u]);
    }
    sort(ps.begin(), ps.end(), [&](const pair<int, int> &p0, const pair<int, int> &p1) -> bool {
      return ((hei[p0.first] != hei[p1.first]) ? (hei[p0.first] > hei[p1.first]) : (p0 < p1));
    });
    const int psLen = ps.size();
  cerr<<"ps = "<<ps<<endl;
    vector<int> ids(N, -1);
    for (int j = 0; j < psLen; ++j) {
      ids[ps[j].first] = ids[ps[j].second] = j;
    }
    
    vector<int> ks(psLen, -1);
    set<int> ss;
    ss.insert(N);
    for (int j = 0; j < psLen; ++j) {
      auto check = [&](int k) -> void {
        if (!~ks[j]) ks[j] = k;
        if (ks[j] != k) ks[j] = -2;
      };
      const int u = ps[j].first;
      const int v = ps[j].second;
      int sz = v - u - 1;
      for (auto it = ss.lower_bound(u); *it < v; it = ss.erase(it)) {
        const int x = *it;
        const int y = mate[x];
        sz -= (y - x + 1);
        check(ks[ids[x]]);
      }
      assert(sz >= 0);
      check(sz);
      ss.insert(u);
    }
  cerr<<"ks = "<<ks<<endl;
    
    for (int j0 = 0, j1 = 0; j0 < psLen; j0 = j1) {
      for (j1 = j0 + 1; j1 < psLen && ps[j1 - 1].second + 1 == ps[j1].first && ks[j1 - 1] == ks[j1]; ++j1) {}
      if (ks[j0] >= 0) {
        ans[ks[j0]] += (Int)(j1 - j0) * (j1 - j0 + 1) / 2;
      }
    }
    
    reverse(C, C + N);
  }
  return ans;
}
}  // sub2


int main() {
  for (; ~scanf("%d%d", &N, &M); ) {
    scanf("%s", C);
    A.resize(N - 1);
    B.resize(N - 1);
    for (int i = 0; i < N - 1; ++i) {
      scanf("%d%d", &A[i], &B[i]);
      --A[i];
      --B[i];
    }
    
    graph.assign(N, {});
    for (int i = 0; i < N - 1; ++i) {
      graph[A[i]].push_back(B[i]);
      graph[B[i]].push_back(A[i]);
    }
    
    bool spe2 = true;
    for (int i = 0; i < N - 1; ++i) {
      spe2 = spe2 && (abs(A[i] - B[i]) == 1);
    }
    
    vector<Int> ans;
    if (spe2) {
      ans = sub2::run();
    } else {
      ans = brute::run();
    }
    for (int k = 0; k <= M; ++k) {
      if (k) printf(" ");
      printf("%lld", ans[k]);
    }
    puts("");
#ifdef LOCAL
const auto brt=brute::run();
if(brt!=ans)cerr<<N<<" "<<M<<" "<<C<<" "<<A<<" "<<B<<": "<<brt<<" "<<ans<<endl;
assert(brt==ans);
#endif
  }
  return 0;
}