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;
  inline int read_int() {
    int t = 0;
    bool sign = false;
    char c = getchar();
    while (!isdigit(c)) {
      sign |= c == '-';
      c = getchar();
    }
    while (isdigit(c)) {
      t = (t << 1) + (t << 3) + (c & 15);
      c = getchar();
    }
    return sign ? -t : t;
  }
  inline long long read_LL() {
    long long t = 0;
    bool sign = false;
    char c = getchar();
    while (!isdigit(c)) {
      sign |= c == '-';
      c = getchar();
    }
    while (isdigit(c)) {
      t = (t << 1) + (t << 3) + (c & 15);
      c = getchar();
    }
    return sign ? -t : t;
  }
  inline char get_char() {
    char c = getchar();
    while (c == ' ' || c == '\n' || c == '\r') c = getchar();
    return c;
  }
  inline void write(long long x) {
    register char c[21], len = 0;
    if (!x) return putchar('0'), void();
    if (x < 0) x = -x, putchar('-');
    while (x) c[++len] = x % 10, x /= 10;
    while (len) putchar(c[len--] + 48);
  }
  inline void space(long long x) { write(x), putchar(' '); }
  inline void enter(long long x) { write(x), putchar('\n'); }
  const int MAXL = 50, MAXM = 5e4 + 5;
  struct opt {
    long long a, b;
    int t;
    bool operator<(const opt &o) const { return a < o.a; }
  };
  vector<opt> upd, nodes;
  void Insert(opt node, long long vl, long long vr) {
    if (node.a == node.b)
      nodes.push_back(node);
    else {
      long long vm = vl + vr >> 1;
      if (node.a <= vm && node.b > vm) {
        nodes.push_back(opt{node.a, vm, node.t});
        nodes.push_back(opt{vm + 1, node.b, node.t});
      } else if (node.b <= vm)
        Insert(node, vl, vm);
      else
        Insert(node, vm + 1, vr);
    }
  }
  vector<pair<int, int> > edges[MAXM];
  void build(int ql, int qr, long long vl, long long vr) {
    if (ql == qr) return;
    long long vm = vl + vr >> 1, len = vm - vl + 1;
    int qm1 = ql, qm2;
    while (qm1 < qr && nodes[qm1 + 1].a <= vm) qm1++;
    qm2 = qm1 + (nodes[qm1].b > vm ? 0 : 1);
    int pos1 = ql, pos2 = qm2;
    while (pos1 <= qm1 && pos2 <= qr) {
      edges[min(nodes[pos1].t, nodes[pos2].t)].emplace_back(pos1, pos2);
      if (nodes[pos1].b + len < nodes[pos2].b)
        pos1++;
      else if (nodes[pos1].b + len > nodes[pos2].b)
        pos2++;
      else
        pos1++, pos2++;
    }
    build(ql, qm1, vl, vm);
    build(qm2, qr, vm + 1, vr);
  }
  int p[MAXM << 2];
  int Find(int x) { return p[x] == x ? x : p[x] = Find(p[x]); }
  pair<long long, long long> query[MAXM];
  vector<long long> mp;
  char buf[MAXL];
  int main() {
    int n = read_int(), m = read_int();
    long long maxv = (1LL << n) - 1;
    for (int i = (0); i < (m); ++i) {
      scanf("%s", buf);
      long long l = read_LL(), r = read_LL();
      if (buf[0] == 'b') {
        upd.push_back(opt{l, r, i});
        query[i] = make_pair(-1LL, -1LL);
      } else
        query[i] = make_pair(l, r);
    }
    query[m] = make_pair(-1LL, -1LL);
    sort(upd.begin(), upd.end());
    long long pos1 = 0;
    int pos2 = 0;
    while (pos1 <= maxv) {
      if (pos2 < upd.size()) {
        if (upd[pos2].a == pos1) {
          Insert(upd[pos2], 0, maxv);
          pos1 = upd[pos2++].b + 1;
        } else {
          Insert(opt{pos1, upd[pos2].a - 1, m}, 0, maxv);
          pos1 = upd[pos2].a;
        }
      } else {
        Insert(opt{pos1, maxv, m}, 0, maxv);
        pos1 = maxv + 1;
      }
    }
    build(0, nodes.size() - 1, 0, maxv);
    for (int i = (0); i < (nodes.size()); ++i) {
      p[i] = i;
      mp.push_back(nodes[i].b);
    }
    stack<int> ans;
    for (int i = m; i >= 0; i--) {
      for (pair<int, int> pr : edges[i]) {
        int x = Find(pr.first), y = Find(pr.second);
        if (x != y) p[x] = y;
      }
      if (query[i].first != -1) {
        int p1 = lower_bound(mp.begin(), mp.end(), query[i].first) - mp.begin();
        int p2 = lower_bound(mp.begin(), mp.end(), query[i].second) - mp.begin();
        p1 = Find(p1);
        p2 = Find(p2);
        if (p1 == p2)
          ans.push(1);
        else
          ans.push(0);
      }
    }
    while (!ans.empty()) {
      enter(ans.top());
      ans.pop();
    }
    return 0;
  }
  