There is little time left before the release of the first national operating system BerlOS. Some of its components are not finished yet — the memory manager is among them. According to the developers' plan, in the first release the memory manager will be very simple and rectilinear. It will support three operations: 

  * alloc n — to allocate n bytes of the memory and return the allocated block's identifier x; 
  * erase x — to erase the block with the identifier x; 
  * defragment — to defragment the free memory, bringing all the blocks as close to the beginning of the memory as possible and preserving their respective order; 



The memory model in this case is very simple. It is a sequence of m bytes, numbered for convenience from the first to the m-th.

The first operation alloc n takes as the only parameter the size of the memory block that is to be allocated. While processing this operation, a free block of n successive bytes is being allocated in the memory. If the amount of such blocks is more than one, the block closest to the beginning of the memory (i.e. to the first byte) is prefered. All these bytes are marked as not free, and the memory manager returns a 32-bit integer numerical token that is the identifier of this block. If it is impossible to allocate a free block of this size, the function returns NULL.

The second operation erase x takes as its parameter the identifier of some block. This operation frees the system memory, marking the bytes of this block as free for further use. In the case when this identifier does not point to the previously allocated block, which has not been erased yet, the function returns ILLEGAL_ERASE_ARGUMENT.

The last operation defragment does not have any arguments and simply brings the occupied memory sections closer to the beginning of the memory without changing their respective order.

In the current implementation you are to use successive integers, starting with 1, as identifiers. Each successful alloc operation procession should return following number. Unsuccessful alloc operations do not affect numeration.

You are to write the implementation of the memory manager. You should output the returned value for each alloc command. You should also output ILLEGAL_ERASE_ARGUMENT for all the failed erase commands.

Input

The first line of the input data contains two positive integers t and m (1 ≤ t ≤ 100;1 ≤ m ≤ 100), where t — the amount of operations given to the memory manager for processing, and m — the available memory size in bytes. Then there follow t lines where the operations themselves are given. The first operation is alloc n (1 ≤ n ≤ 100), where n is an integer. The second one is erase x, where x is an arbitrary 32-bit integer numerical token. The third operation is defragment. 

Output

Output the sequence of lines. Each line should contain either the result of alloc operation procession , or ILLEGAL_ERASE_ARGUMENT as a result of failed erase operation procession. Output lines should go in the same order in which the operations are processed. Successful procession of alloc operation should return integers, starting with 1, as the identifiers of the allocated blocks.

Examples

Input

6 10
alloc 5
alloc 3
erase 1
alloc 6
defragment
alloc 6


Output

1
2
NULL
3
#include <bits/stdc++.h>
using namespace std;
namespace teorNum {
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
template <typename num>
int sign(num n) {
  return n >= 0 ? 1 : -1;
}
}  // namespace teorNum
namespace geom {
inline bool doubleEqual(double a, double b, double eps = 0.001) {
  return abs(a / b - 1) <= eps;
}
const double pi = std::atan(1.0f) * 4;
class vec {
 public:
  vec() = default;
  vec(int len) : data(len){};
  vec(double x, double y) : data({x, y}){};
  vec(double x, double y, double z) : data({x, y, z}){};
  vec(const vec& temp) : data(temp.data) {}
  vec(const std::initializer_list<double>& list) {
    for (auto& element : list) data.push_back(element);
  }
  friend const vec& operator+(const vec& left);
  friend const vec operator-(const vec& left);
  friend vec& operator+=(vec& left, const vec& right);
  friend vec& operator-=(vec& left, const vec& right);
  friend vec& operator*=(vec& left, const double right);
  friend vec& operator/=(vec& left, const double right);
  friend bool operator==(const vec& left, const vec& right);
  friend bool operator!=(const vec& left, const vec& right);
  double& operator[](int i) { return data[i]; };
  const double& operator[](int i) const { return data[i]; };
  vec& operator=(const vec& right) {
    data = right.data;
    return *this;
  };
  friend const vec operator+(const vec& left, const vec& right);
  friend const vec operator-(const vec& left, const vec& right);
  friend const vec operator*(const vec& left, const double right);
  friend const vec operator*(const double left, const vec& right);
  friend const vec operator/(const vec& left, const double right);
  friend const vec operator/(const double left, const vec& right);
  friend ostream& operator<<(ostream& out, const vec& a);
  friend istream& operator>>(istream& in, vec& a);
  int size() const { return data.size(); };
  double length() const {
    double sum = 0;
    for (int i = 0; i < size(); ++i) sum += (data[i] * data[i]);
    return sqrt(sum);
  }
  double scalarMupltiply(const vec& right) const {
    double ans = 0;
    for (int i = 0; i < size(); ++i) ans += (data[i] * right[i]);
    return ans;
  }
  const vec vectorMultiply(const vec& right) const {
    if (size() != right.size()) throw "Different sizes";
    if (size() < 2 || size() > 3) throw "Wrong size";
    vec a(3), b(3);
    if (size() == 2) {
      a = {data[0], data[1], 0};
      b = {right[0], right[1], 0};
    } else {
      a = *this;
      b = right;
    }
    vec ans(3);
    ans = {a[1] * b[2] - a[2] * b[1], -a[0] * b[2] + a[2] * b[0],
           a[0] * b[1] - a[1] * b[0]};
    return ans;
  }
  double angle() { return acos(scalarMupltiply({1, 0}) / length()); };
  double angleBetweenVectors(const vec& b) {
    return acos(scalarMupltiply(b) / b.length() / length());
  };
  const vec rotate(double angle) {
    return {data[0] * cos(angle) - data[1] * sin(angle),
            data[0] * sin(angle) + data[1] * cos(angle)};
  };

 private:
  vector<double> data;
};
const vec& operator+(const vec& left) { return left; };
const vec operator-(const vec& left) {
  vec temp(left);
  return temp *= -1;
};
vec& operator+=(vec& left, const vec& right) {
  if (left.size() != right.size()) throw "Different sizes";
  for (int i = 0; i < left.size(); ++i) left[i] += right[i];
  return left;
}
vec& operator-=(vec& left, const vec& right) { return left += (-right); };
vec& operator*=(vec& left, const double right) {
  for (int i = 0; i < left.size(); ++i) left[i] *= right;
  return left;
}
vec& operator/=(vec& left, const double right) {
  for (int i = 0; i < left.size(); ++i) left[i] /= right;
  return left;
}
bool operator==(const vec& left, const vec& right) {
  for (int i = 0; i < left.size(); ++i)
    if (!doubleEqual(left[i], right[i])) return 0;
  return 1;
};
bool operator!=(const vec& left, const vec& right) { return !(left == right); }
const vec operator+(const vec& left, const vec& right) {
  vec temp = left;
  return temp += right;
}
const vec operator-(const vec& left, const vec& right) {
  return left + (-right);
}
const vec operator*(const vec& left, const double right) {
  vec temp = left;
  return temp *= right;
}
const vec operator*(const double left, const vec& right) {
  vec temp = right;
  return temp *= left;
}
const vec operator/(const vec& left, const double right) {
  vec temp = left;
  return temp /= right;
}
const vec operator/(const double left, const vec& right) {
  vec temp = right;
  return temp *= left;
}
ostream& operator<<(ostream& out, const vec& a) {
  for (int i = 0; i < a.size(); ++i) out << a[i] << " ";
  return out;
}
istream& operator>>(istream& in, vec& a) {
  for (int i = 0; i < a.size(); ++i) in >> a[i];
  return in;
}
double square(const std::initializer_list<vec>& list) {
  vec ans((list.end() - 1)->vectorMultiply(*list.begin()));
  for (auto iter = list.begin(); iter != list.end() - 1; ++iter)
    ans += (*iter).vectorMultiply(*(iter + 1));
  return ans.length() / 2;
}
}  // namespace geom
using namespace geom;
using namespace teorNum;
void solution() {
  long long t, m;
  cin >> t >> m;
  vector<long long> memory(m + 1, 0);
  memory[0] = 1;
  long long historyCount = 0;
  vector<long long> history(t + 2, -1);
  vector<long long> historyLen(t + 2, -1);
  for (int i = 0; i < t; ++i) {
    string command;
    cin >> command;
    if (command == "defragment") {
      long long start = 1;
      for (int i1 = 1; i1 <= m; ++i1) {
        int i2 = 1;
        if (memory[i1] == 1) {
          for (i2 = 1; i2 <= t; ++i2) {
            if (history[i2] == i1) break;
          }
          for (int i3 = 0; i3 < historyLen[i2]; ++i3) {
            swap(memory[i3 + start], memory[history[i2] + i3]);
          }
          history[i2] = start;
          start += historyLen[i2];
          i1 = start - 1;
        }
      }
      continue;
    }
    long long count;
    cin >> count;
    if (command == "alloc") {
      long long start = 1;
      int i1 = 1;
      for (i1 = 1; i1 <= m; ++i1) {
        if (memory[i1] == 0 && memory[i1 - 1] == 1) start = i1;
        if (memory[i1] == 0 && i1 - start + 1 >= count) {
          for (int i3 = start; i3 < start + count; ++i3) memory[i3] = 1;
          history[++historyCount] = start;
          historyLen[historyCount] = count;
          cout << historyCount << endl;
          break;
        }
        if (memory[i1] == 1) {
          start = 1000;
        }
      }
      if (i1 == m + 1) cout << "NULL" << endl;
    }
    if (command == "erase") {
      if (count < 1 || count >= t) {
        cout << "ILLEGAL_ERASE_ARGUMENT" << endl;
        continue;
      }
      if (history[count] == -1) {
        cout << "ILLEGAL_ERASE_ARGUMENT" << endl;
        continue;
      } else {
        for (int i1 = history[count]; i1 < history[count] + historyLen[count];
             ++i1) {
          memory[i1] = 0;
        }
        history[count] = -1;
        historyLen[count] = -1;
      }
    }
  }
}
int main() { solution(); }
