#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct Query {
  char q;
  ll a;
  ll b;
};
int gf(vector<int>& f, int cur) {
  int root = cur;
  while (f[root] >= 0) {
    root = f[root];
  }
  int next = f[cur];
  while (next >= 0) {
    f[cur] = root;
    cur = next;
    next = f[cur];
  }
  return root;
}
void mf(vector<int>& f, int a, int b) {
  a = gf(f, a);
  b = gf(f, b);
  if (a == b) {
    return;
  }
  f[a] = b;
}
int is_pow2(ll n) { return (n & (n - 1)) == 0; }
int main() {
  std::ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<Query> q(m);
  for (int i = 0; i < m; ++i) {
    string s;
    cin >> s >> q[i].a >> q[i].b;
    q[i].q = s[0];
  }
  set<ll> pts;
  pts.insert(0);
  pts.insert((1ll << (n)));
  for (int i = 0; i < m; ++i) {
    if (q[i].q == 'b') {
      ll a = q[i].a;
      ll b = q[i].b + 1;
      pts.insert(a);
      pts.insert(b);
    }
  }
  vector<ll> pre_vals(pts.begin(), pts.end());
  for (int i = 0; i + 1 < pre_vals.size(); ++i) {
    ll a = pre_vals[i];
    ll b = pre_vals[i + 1];
    while (a < b) {
      for (int i = n - 1; i >= 0; --i) {
        if ((a & ((1ll << (i)) - 1)) == 0 && a + (1ll << (i)) <= b) {
          a += (1ll << (i));
          pts.insert(a);
          break;
        }
      }
    }
  }
  vector<int> ret(m);
  vector<ll> vals(pts.begin(), pts.end());
  vector<int> f(vals.size(), -1);
  vector<int> ok(vals.size());
  vector<int> bad(vals.size());
  for (int i = m - 1; i >= 0; --i) {
    if (q[i].q == 'b') {
      ll a = q[i].a;
      ll b = q[i].b + 1;
      int idx = lower_bound(vals.begin(), vals.end(), a) - vals.begin();
      for (; idx < vals.size() && vals[idx] < b; ++idx) {
        bad[idx] = 1;
      }
    }
  }
  int total = 0;
  vector<int> logw(vals.size());
  for (int i = 0; i + 1 < vals.size(); ++i) {
    ll w = vals[i + 1] - vals[i];
    int b = 0;
    while (w != 1) {
      ++b;
      w >>= 1;
    }
    logw[i] = b;
  }
  auto recover = [&](int idx) {
    assert(!ok[idx]);
    ok[idx] = 1;
    ll cur = vals[idx];
    int l_idx = logw[idx];
    for (int bit = l_idx; bit < n; ++bit) {
      ll next = (cur ^ (1ll << (bit)));
      int i = upper_bound(vals.begin(), vals.end(), next) - vals.begin() - 1;
      for (; i + 1 < vals.size(); ++i) {
        int l_i = logw[i];
        ll diff = ((vals[idx] ^ vals[i]) >> max(l_idx, l_i));
        if (!is_pow2(diff)) {
          break;
        }
        if (ok[i]) {
          ++total;
          mf(f, idx, i);
        }
      }
    }
  };
  for (int i = 0; i + 1 < vals.size(); ++i) {
    if (!bad[i]) {
      recover(i);
    }
  }
  for (int i = m - 1; i >= 0; --i) {
    if (q[i].q == 'b') {
      ll a = q[i].a;
      ll b = q[i].b + 1;
      int idx = lower_bound(vals.begin(), vals.end(), a) - vals.begin();
      for (; idx < vals.size() && vals[idx] < b; ++idx) {
        recover(idx);
      }
    } else {
      ll a = q[i].a;
      ll b = q[i].b;
      int idx_a = upper_bound(vals.begin(), vals.end(), a) - vals.begin() - 1;
      int idx_b = upper_bound(vals.begin(), vals.end(), b) - vals.begin() - 1;
      assert(ok[idx_a]);
      assert(ok[idx_b]);
      ret[i] = (gf(f, idx_a) == gf(f, idx_b) ? 1 : 0);
    }
  }
  for (int i = 0; i < m; ++i) {
    if (q[i].q == 'a') {
      printf("%d\n", ret[i]);
    }
  }
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

<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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct Query {
  char q;
  ll a;
  ll b;
};
int gf(vector<int>& f, int cur) {
  int root = cur;
  while (f[root] >= 0) {
    root = f[root];
  }
  int next = f[cur];
  while (next >= 0) {
    f[cur] = root;
    cur = next;
    next = f[cur];
  }
  return root;
}
void mf(vector<int>& f, int a, int b) {
  a = gf(f, a);
  b = gf(f, b);
  if (a == b) {
    return;
  }
  f[a] = b;
}
int is_pow2(ll n) { return (n & (n - 1)) == 0; }
int main() {
  std::ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<Query> q(m);
  for (int i = 0; i < m; ++i) {
    string s;
    cin >> s >> q[i].a >> q[i].b;
    q[i].q = s[0];
  }
  set<ll> pts;
  pts.insert(0);
  pts.insert((1ll << (n)));
  for (int i = 0; i < m; ++i) {
    if (q[i].q == 'b') {
      ll a = q[i].a;
      ll b = q[i].b + 1;
      pts.insert(a);
      pts.insert(b);
    }
  }
  vector<ll> pre_vals(pts.begin(), pts.end());
  for (int i = 0; i + 1 < pre_vals.size(); ++i) {
    ll a = pre_vals[i];
    ll b = pre_vals[i + 1];
    while (a < b) {
      for (int i = n - 1; i >= 0; --i) {
        if ((a & ((1ll << (i)) - 1)) == 0 && a + (1ll << (i)) <= b) {
          a += (1ll << (i));
          pts.insert(a);
          break;
        }
      }
    }
  }
  vector<int> ret(m);
  vector<ll> vals(pts.begin(), pts.end());
  vector<int> f(vals.size(), -1);
  vector<int> ok(vals.size());
  vector<int> bad(vals.size());
  for (int i = m - 1; i >= 0; --i) {
    if (q[i].q == 'b') {
      ll a = q[i].a;
      ll b = q[i].b + 1;
      int idx = lower_bound(vals.begin(), vals.end(), a) - vals.begin();
      for (; idx < vals.size() && vals[idx] < b; ++idx) {
        bad[idx] = 1;
      }
    }
  }
  int total = 0;
  vector<int> logw(vals.size());
  for (int i = 0; i + 1 < vals.size(); ++i) {
    ll w = vals[i + 1] - vals[i];
    int b = 0;
    while (w != 1) {
      ++b;
      w >>= 1;
    }
    logw[i] = b;
  }
  auto recover = [&](int idx) {
    assert(!ok[idx]);
    ok[idx] = 1;
    ll cur = vals[idx];
    int l_idx = logw[idx];
    for (int bit = l_idx; bit < n; ++bit) {
      ll next = (cur ^ (1ll << (bit)));
      int i = upper_bound(vals.begin(), vals.end(), next) - vals.begin() - 1;
      for (; i + 1 < vals.size(); ++i) {
        int l_i = logw[i];
        ll diff = ((vals[idx] ^ vals[i]) >> max(l_idx, l_i));
        if (!is_pow2(diff)) {
          break;
        }
        if (ok[i]) {
          ++total;
          mf(f, idx, i);
        }
      }
    }
  };
  for (int i = 0; i + 1 < vals.size(); ++i) {
    if (!bad[i]) {
      recover(i);
    }
  }
  for (int i = m - 1; i >= 0; --i) {
    if (q[i].q == 'b') {
      ll a = q[i].a;
      ll b = q[i].b + 1;
      int idx = lower_bound(vals.begin(), vals.end(), a) - vals.begin();
      for (; idx < vals.size() && vals[idx] < b; ++idx) {
        recover(idx);
      }
    } else {
      ll a = q[i].a;
      ll b = q[i].b;
      int idx_a = upper_bound(vals.begin(), vals.end(), a) - vals.begin() - 1;
      int idx_b = upper_bound(vals.begin(), vals.end(), b) - vals.begin() - 1;
      assert(ok[idx_a]);
      assert(ok[idx_b]);
      ret[i] = (gf(f, idx_a) == gf(f, idx_b) ? 1 : 0);
    }
  }
  for (int i = 0; i < m; ++i) {
    if (q[i].q == 'a') {
      printf("%d\n", ret[i]);
    }
  }
  return 0;
}

```