description: <image>
  
  As mentioned previously William really likes playing video games. In one of his favorite games, the player character is in a universe where every planet is designated by a binary number from 0 to 2^n - 1. On each planet, there are gates that allow the player to move from planet i to planet j if the binary representations of i and j differ in exactly one bit.
  
  William wants to test you and see how you can handle processing the following queries in this game universe:
  
    * Destroy planets with numbers from l to r inclusively. These planets cannot be moved to anymore.
    * Figure out if it is possible to reach planet b from planet a using some number of planetary gates. It is guaranteed that the planets a and b are not destroyed. 
  
  Input
  
  The first line contains two integers n, m (1 ≤ n ≤ 50, 1 ≤ m ≤ 5 ⋅ 10^4), which are the number of bits in binary representation of each planets' designation and the number of queries, respectively.
  
  Each of the next m lines contains a query of two types:
  
  block l r — query for destruction of planets with numbers from l to r inclusively (0 ≤ l ≤ r < 2^n). It's guaranteed that no planet will be destroyed twice.
  
  ask a b — query for reachability between planets a and b (0 ≤ a, b < 2^n). It's guaranteed that planets a and b hasn't been destroyed yet.
  
  Output
  
  For each query of type ask you must output "1" in a new line, if it is possible to reach planet b from planet a and "0" otherwise (without quotation marks).
  
  Examples
  
  Input
  
  
  3 3
  ask 0 7
  block 3 6
  ask 0 7
  
  
  Output
  
  
  1
  0
  
  
  Input
  
  
  6 10
  block 12 26
  ask 44 63
  block 32 46
  ask 1 54
  block 27 30
  ask 10 31
  ask 11 31
  ask 49 31
  block 31 31
  ask 2 51
  
  
  Output
  
  
  1
  1
  0
  0
  1
  0
  
  Note
  
  The first example test can be visualized in the following way:
  
  <image>
  
  Response to a query ask 0 7 is positive.
  
  Next after query block 3 6 the graph will look the following way (destroyed vertices are highlighted):
  
  <image>
  
  Response to a query ask 0 7 is negative, since any path from vertex 0 to vertex 7 must go through one of the destroyed vertices.
solution: #include <bits/stdc++.h>
  const int M = 5e4 + 5;
  const int N = M << 6;
  int n, m;
  int ans[M];
  long long U;
  struct query {
    std::string opt;
    long long x, y;
  } qry[M];
  std::vector<std::pair<int, int>> edge[M];
  int tot = 1, lc[N], rc[N];
  int rec[N], uset[N];
  int find(int x) { return x == uset[x] ? x : uset[x] = find(uset[x]); }
  bool flag = 0;
  void pushdown(int x) {
    if (!lc[x]) lc[x] = ++tot, assert(!flag);
    if (!rc[x]) rc[x] = ++tot, assert(!flag);
    if (rec[x]) rec[lc[x]] = rec[rc[x]] = rec[x], rec[x] = 0;
  }
  void insert(int x, long long l, long long r, long long ql, long long qr,
              int t) {
    if (ql > r || l > qr) return;
    if (ql <= l && r <= qr) {
      rec[x] = t;
      return;
    }
    pushdown(x);
    insert(lc[x], l, ((l + r) >> 1), ql, qr, t);
    insert(rc[x], ((l + r) >> 1) + 1, r, ql, qr, t);
  }
  void complete(int x) {
    if (!lc[x] && !rc[x]) return;
    pushdown(x);
    complete(lc[x]);
    complete(rc[x]);
  }
  void connect(int x, int y) {
    if ((!lc[x] && !rc[x]) && (!lc[y] && !rc[y]))
      return (void)edge[std::min(rec[x], rec[y])].emplace_back(x, y);
    if ((!lc[x] && !rc[x])) return connect(x, lc[y]), connect(x, rc[y]);
    if ((!lc[y] && !rc[y])) return connect(lc[x], y), connect(rc[x], y);
    connect(lc[x], lc[y]), connect(rc[x], rc[y]);
  }
  int locate(int x, long long l, long long r, long long p) {
    if ((!lc[x] && !rc[x])) return x;
    if (p <= ((l + r) >> 1))
      return locate(lc[x], l, ((l + r) >> 1), p);
    else
      return locate(rc[x], ((l + r) >> 1) + 1, r, p);
  }
  signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    std::cin >> n >> m;
    U = (1ll << n) - 1;
    rec[1] = m + 1;
    for (int i = 1; i <= m; i++) {
      std::cin >> qry[i].opt >> qry[i].x >> qry[i].y;
      if (qry[i].opt == "block") insert(1, 0, U, qry[i].x, qry[i].y, i);
    }
    flag = 1;
    for (int i = 1; i <= tot; i++)
      if (!(!lc[i] && !rc[i])) connect(lc[i], rc[i]);
    for (int i = 1; i <= tot; i++) uset[i] = i;
    for (auto [x, y] : edge[m + 1]) uset[find(x)] = find(y);
    for (int i = m; i; --i) {
      for (auto [x, y] : edge[i]) uset[find(x)] = find(y);
      if (qry[i].opt == "ask")
        ans[i] =
            find(locate(1, 0, U, qry[i].x)) == find(locate(1, 0, U, qry[i].y));
    }
    for (int i = 1; i <= m; i++)
      if (qry[i].opt == "ask") std::cout << ans[i] << "\n";
    return 0;
  }
  