#include <bits/stdc++.h>
using namespace std;
int n, m;
const int maxN = 5e4 + 10;
int tp[maxN];
long long l[maxN], r[maxN];
vector<pair<long long, long long>> segs;
void rec(int bit, long long l, long long r) {
  long long all = (1LL << (bit + 1)) - 1;
  long long msk1 = l & all;
  long long msk2 = r & all;
  if (msk1 == 0 && msk2 == all) {
    segs.emplace_back(l, r);
    return;
  }
  if (msk1 >= (1LL << bit)) {
    rec(bit - 1, l, r);
  } else if (msk2 < (1LL << bit)) {
    rec(bit - 1, l, r);
  } else {
    long long f = l | ((1LL << bit) - 1);
    assert(l <= f && f + 1 <= r);
    rec(bit - 1, l, f);
    rec(bit - 1, f + 1, r);
  }
}
vector<pair<int, int>> to_add[maxN];
const int maxK = 2e6;
int p[maxK];
int sz[maxK];
int get(int x) {
  if (x == p[x]) return x;
  return p[x] = get(p[x]);
}
void unite(int a, int b) {
  a = get(a);
  b = get(b);
  if (a == b) return;
  if (sz[a] < sz[b]) swap(a, b);
  p[b] = a;
  sz[a] += sz[b];
}
bool ans[maxN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n >> m;
  vector<pair<long long, long long>> f;
  for (int i = 1; i <= m; i++) {
    string s;
    cin >> s;
    if (s == "ask")
      tp[i] = 0;
    else
      tp[i] = 1;
    cin >> l[i] >> r[i];
    if (tp[i] == 1) f.emplace_back(l[i], r[i]);
  }
  sort(f.begin(), f.end());
  if (f.empty()) {
    f.emplace_back(0, (1LL << n) - 1);
  }
  vector<pair<long long, long long>> nf;
  if (f[0].first != 0) {
    nf.emplace_back(0, f[0].first - 1);
  }
  for (int i = 0; i < f.size(); i++) {
    nf.emplace_back(f[i]);
    if (i + 1 < f.size() && f[i].second + 1 <= f[i + 1].first - 1)
      nf.emplace_back(f[i].second + 1, f[i + 1].first - 1);
  }
  if (f.back().second + 1 <= (1LL << n) - 1) {
    nf.emplace_back(f.back().second + 1, (1LL << n) - 1);
  }
  for (auto& it : nf) {
    rec(n - 1, it.first, it.second);
  }
  vector<int> ti(segs.size(), -1);
  for (int i = 1; i <= m; i++) {
    if (tp[i] == 1) {
      int pos1 = lower_bound(segs.begin(), segs.end(), make_pair(l[i], -1LL)) -
                 segs.begin();
      int pos2 =
          lower_bound(segs.begin(), segs.end(), make_pair(r[i] + 1, -1LL)) -
          segs.begin();
      for (int z = pos1; z < pos2; z++) {
        ti[z] = i;
      }
    }
  }
  for (int i = 0; i < segs.size(); i++) {
    if (ti[i] == -1) {
      ti[i] = m;
    }
  }
  for (int bit = 0; bit < n; bit++) {
    vector<int> group[2];
    for (int id = 0; id < segs.size(); id++) {
      long long l = segs[id].first;
      long long r = segs[id].second;
      if (r - l + 1 <= (1LL << bit)) {
        assert((l & (1LL << bit)) == (r & (1LL << bit)));
        group[(l >> bit) & 1].emplace_back(id);
      }
    }
    for (int z = 0; z < 2; z++) {
      int ptr = 0;
      for (int p : group[z]) {
        long long f = segs[p].first ^ (1LL << bit);
        while (segs[ptr].second < f) ptr++;
        if (segs[ptr].second - segs[ptr].first >=
            segs[p].second - segs[p].first) {
          to_add[min(ti[ptr], ti[p])].emplace_back(ptr, p);
        }
      }
    }
  }
  assert(segs.size() < maxK);
  for (int i = 0; i < segs.size(); i++) {
    p[i] = i;
    sz[i] = 1;
  }
  for (int i = m; i >= 1; i--) {
    for (auto& it : to_add[i]) {
      unite(it.first, it.second);
    }
    if (tp[i] == 0) {
      int p1 =
          upper_bound(segs.begin(), segs.end(), make_pair(l[i] + 1, -1LL)) -
          segs.begin() - 1;
      int p2 =
          upper_bound(segs.begin(), segs.end(), make_pair(r[i] + 1, -1LL)) -
          segs.begin() - 1;
      if (get(p1) == get(p2)) {
        ans[i] = true;
      } else {
        ans[i] = false;
      }
    }
  }
  for (int i = 1; i <= m; i++) {
    if (tp[i] == 0) {
      cout << ans[i] << '\n';
    }
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

<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;
int n, m;
const int maxN = 5e4 + 10;
int tp[maxN];
long long l[maxN], r[maxN];
vector<pair<long long, long long>> segs;
void rec(int bit, long long l, long long r) {
  long long all = (1LL << (bit + 1)) - 1;
  long long msk1 = l & all;
  long long msk2 = r & all;
  if (msk1 == 0 && msk2 == all) {
    segs.emplace_back(l, r);
    return;
  }
  if (msk1 >= (1LL << bit)) {
    rec(bit - 1, l, r);
  } else if (msk2 < (1LL << bit)) {
    rec(bit - 1, l, r);
  } else {
    long long f = l | ((1LL << bit) - 1);
    assert(l <= f && f + 1 <= r);
    rec(bit - 1, l, f);
    rec(bit - 1, f + 1, r);
  }
}
vector<pair<int, int>> to_add[maxN];
const int maxK = 2e6;
int p[maxK];
int sz[maxK];
int get(int x) {
  if (x == p[x]) return x;
  return p[x] = get(p[x]);
}
void unite(int a, int b) {
  a = get(a);
  b = get(b);
  if (a == b) return;
  if (sz[a] < sz[b]) swap(a, b);
  p[b] = a;
  sz[a] += sz[b];
}
bool ans[maxN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n >> m;
  vector<pair<long long, long long>> f;
  for (int i = 1; i <= m; i++) {
    string s;
    cin >> s;
    if (s == "ask")
      tp[i] = 0;
    else
      tp[i] = 1;
    cin >> l[i] >> r[i];
    if (tp[i] == 1) f.emplace_back(l[i], r[i]);
  }
  sort(f.begin(), f.end());
  if (f.empty()) {
    f.emplace_back(0, (1LL << n) - 1);
  }
  vector<pair<long long, long long>> nf;
  if (f[0].first != 0) {
    nf.emplace_back(0, f[0].first - 1);
  }
  for (int i = 0; i < f.size(); i++) {
    nf.emplace_back(f[i]);
    if (i + 1 < f.size() && f[i].second + 1 <= f[i + 1].first - 1)
      nf.emplace_back(f[i].second + 1, f[i + 1].first - 1);
  }
  if (f.back().second + 1 <= (1LL << n) - 1) {
    nf.emplace_back(f.back().second + 1, (1LL << n) - 1);
  }
  for (auto& it : nf) {
    rec(n - 1, it.first, it.second);
  }
  vector<int> ti(segs.size(), -1);
  for (int i = 1; i <= m; i++) {
    if (tp[i] == 1) {
      int pos1 = lower_bound(segs.begin(), segs.end(), make_pair(l[i], -1LL)) -
                 segs.begin();
      int pos2 =
          lower_bound(segs.begin(), segs.end(), make_pair(r[i] + 1, -1LL)) -
          segs.begin();
      for (int z = pos1; z < pos2; z++) {
        ti[z] = i;
      }
    }
  }
  for (int i = 0; i < segs.size(); i++) {
    if (ti[i] == -1) {
      ti[i] = m;
    }
  }
  for (int bit = 0; bit < n; bit++) {
    vector<int> group[2];
    for (int id = 0; id < segs.size(); id++) {
      long long l = segs[id].first;
      long long r = segs[id].second;
      if (r - l + 1 <= (1LL << bit)) {
        assert((l & (1LL << bit)) == (r & (1LL << bit)));
        group[(l >> bit) & 1].emplace_back(id);
      }
    }
    for (int z = 0; z < 2; z++) {
      int ptr = 0;
      for (int p : group[z]) {
        long long f = segs[p].first ^ (1LL << bit);
        while (segs[ptr].second < f) ptr++;
        if (segs[ptr].second - segs[ptr].first >=
            segs[p].second - segs[p].first) {
          to_add[min(ti[ptr], ti[p])].emplace_back(ptr, p);
        }
      }
    }
  }
  assert(segs.size() < maxK);
  for (int i = 0; i < segs.size(); i++) {
    p[i] = i;
    sz[i] = 1;
  }
  for (int i = m; i >= 1; i--) {
    for (auto& it : to_add[i]) {
      unite(it.first, it.second);
    }
    if (tp[i] == 0) {
      int p1 =
          upper_bound(segs.begin(), segs.end(), make_pair(l[i] + 1, -1LL)) -
          segs.begin() - 1;
      int p2 =
          upper_bound(segs.begin(), segs.end(), make_pair(r[i] + 1, -1LL)) -
          segs.begin() - 1;
      if (get(p1) == get(p2)) {
        ans[i] = true;
      } else {
        ans[i] = false;
      }
    }
  }
  for (int i = 1; i <= m; i++) {
    if (tp[i] == 0) {
      cout << ans[i] << '\n';
    }
  }
  return 0;
}

```