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>
  using namespace std;
  int n, m, len, ans[400020];
  long long b[400020];
  vector<int> G[400020];
  bool vis[400020], live[400020];
  inline void adde(int u, int v) {
    G[u].push_back(v);
    G[v].push_back(u);
  }
  struct Query {
    long long l, r;
    int opt;
  } q[400020];
  class Union_Set {
    inline int lowbit(int x) { return x & (-x); }
  
   public:
    int f[400020];
    void init(int n) {
      for (int i = 1; i <= n; ++i) f[i] = i;
    }
    inline int getf(int x) { return f[x] == x ? x : f[x] = getf(f[x]); }
    inline void Merge(int x, int y) {
      int fx = getf(x), fy = getf(y);
      if (fx ^ fy) f[fy] = fx;
    }
  } S;
  void Insert(int u) {
    live[u] = 1;
    for (auto v : G[u])
      if (live[v]) S.Merge(u, v);
  }
  int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> m;
    b[len = 1] = 0;
    for (int i = 1; i <= m; ++i) {
      string s;
      cin >> s;
      cin >> q[i].l >> q[i].r;
      q[i].opt = s[0] == 'b';
      if (q[i].opt) {
        b[++len] = q[i].l, b[++len] = q[i].r + 1;
      }
    }
    b[++len] = 1LL << n;
    sort(b + 1, b + len + 1);
    for (int i = 1, jb = len; i < jb; ++i) {
      long long l = b[i], r = b[i + 1] - 1;
      if (l >= r) continue;
      long long x = 1LL << (63 - __builtin_clzll(l ^ r));
      b[++len] = x | (l ^ (l & (x - 1)));
    }
    sort(b + 1, b + len + 1);
    len = unique(b + 1, b + len + 1) - b - 2;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j <= 1; ++j) {
        for (int k = 1, p = 1; k <= len; ++k) {
          if ((b[k] >> i & 1) == j) {
            long long v = b[k] ^ (1LL << i);
            while (v >= b[p + 1]) ++p;
            if (p ^ k) adde(p, k);
          }
        }
      }
    }
    for (int i = 1; i <= m; ++i) {
      if (q[i].opt) {
        int l = lower_bound(b + 1, b + len + 1, q[i].l) - b;
        int r = upper_bound(b + 1, b + len + 1, q[i].r) - b - 1;
        for (int j = l; j <= r; ++j) vis[j] = 1;
      }
    }
    S.init(len);
    for (int i = 1; i <= len; ++i) {
      if (!vis[i]) Insert(i);
    }
    for (int i = m; i >= 1; --i) {
      if (q[i].opt) {
        int l = lower_bound(b + 1, b + len + 1, q[i].l) - b;
        int r = upper_bound(b + 1, b + len + 1, q[i].r) - b - 1;
        for (int j = l; j <= r; ++j) Insert(j);
      } else {
        int u = upper_bound(b + 1, b + len + 1, q[i].l) - b - 1;
        int v = upper_bound(b + 1, b + len + 1, q[i].r) - b - 1;
        ans[i] = S.getf(u) == S.getf(v);
      }
    }
    for (int i = 1; i <= m; ++i) {
      if (!q[i].opt) cout << ans[i] << '\n';
    }
    return 0;
  }
  