#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
double PI = acos(-1);
namespace {
template <typename T>
std::ostream &operator<<(std::ostream &, const std::vector<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::deque<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::set<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::stack<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::queue<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::priority_queue<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::unordered_set<T> &);
template <typename T, typename U>
std::ostream &operator<<(std::ostream &, const std::map<T, U> &);
template <typename T, typename U>
std::ostream &operator<<(std::ostream &, const std::unordered_map<T, U> &);
template <typename T, typename U>
std::ostream &operator<<(std::ostream &, const std::pair<T, U> &);
template <typename... T>
std::ostream &operator<<(std::ostream &, const std::tuple<T...> &);
template <typename T, std::size_t N>
std::ostream &operator<<(std::ostream &, const std::array<T, N> &);
template <typename Tuple, std::size_t N>
struct __TuplePrinter__ {
  static void print(std::ostream &os, const Tuple &t) {
    __TuplePrinter__<Tuple, N - 1>::print(os, t);
    os << ", " << std::get<N - 1>(t);
  }
};
template <typename Tuple>
struct __TuplePrinter__<Tuple, 1> {
  static void print(std::ostream &os, const Tuple &t) { os << std::get<0>(t); }
};
template <typename... T>
std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) {
  os << '(';
  __TuplePrinter__<decltype(t), sizeof...(T)>::print(os, t);
  os << ')';
  return os;
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &v) {
  return os << '(' << v.first << ", " << v.second << ')';
}
template <typename T, std::size_t N>
std::ostream &operator<<(std::ostream &os, const std::array<T, N> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::deque<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::set<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::stack<T> &c) {
  std::deque<T> v;
  for (auto d = c; !d.empty(); d.pop()) v.push_front(d.top());
  return os << v;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::queue<T> &c) {
  std::deque<T> v;
  for (auto d = c; !d.empty(); d.pop()) v.push_back(d.front());
  return os << v;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::priority_queue<T> &c) {
  std::deque<T> v;
  for (auto d = c; !d.empty(); d.pop()) v.push_front(d.top());
  return os << v;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::unordered_set<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::map<T, U> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::unordered_map<T, U> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
}  // namespace
template <signed M, unsigned T>
struct mod_int {
  constexpr static signed MODULO = M;
  constexpr static unsigned TABLE_SIZE = T;
  signed x;
  mod_int() : x(0) {}
  mod_int(long long y)
      : x(static_cast<signed>(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) {}
  mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) {}
  mod_int &operator+=(const mod_int &rhs) {
    if ((x += rhs.x) >= MODULO) x -= MODULO;
    return *this;
  }
  mod_int &operator-=(const mod_int &rhs) {
    if ((x += MODULO - rhs.x) >= MODULO) x -= MODULO;
    return *this;
  }
  mod_int &operator*=(const mod_int &rhs) {
    x = static_cast<signed>(1LL * x * rhs.x % MODULO);
    return *this;
  }
  mod_int &operator/=(const mod_int &rhs) {
    x = static_cast<signed>((1LL * x * rhs.inv().x) % MODULO);
    return *this;
  }
  mod_int operator-() const { return mod_int(-x); }
  mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; }
  mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; }
  mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; }
  mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; }
  bool operator<(const mod_int &rhs) const { return x < rhs.x; }
  mod_int inv() const {
    assert(x != 0);
    if (x <= static_cast<signed>(TABLE_SIZE)) {
      if (_inv[1].x == 0) prepare();
      return _inv[x];
    } else {
      signed a = x, b = MODULO, u = 1, v = 0, t;
      while (b) {
        t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }
      return mod_int(u);
    }
  }
  mod_int pow(long long t) const {
    assert(!(x == 0 && t == 0));
    mod_int e = *this, res = mod_int(1);
    for (; t; e *= e, t >>= 1)
      if (t & 1) res *= e;
    return res;
  }
  mod_int fact() {
    if (_fact[0].x == 0) prepare();
    return _fact[x];
  }
  mod_int inv_fact() {
    if (_fact[0].x == 0) prepare();
    return _inv_fact[x];
  }
  mod_int choose(mod_int y) {
    assert(y.x <= x);
    return this->fact() * y.inv_fact() * mod_int(x - y.x).inv_fact();
  }
  static mod_int _inv[TABLE_SIZE + 1];
  static mod_int _fact[TABLE_SIZE + 1];
  static mod_int _inv_fact[TABLE_SIZE + 1];
  static void prepare() {
    _inv[1] = 1;
    for (int i = 2; i <= (int)TABLE_SIZE; ++i) {
      _inv[i] = 1LL * _inv[MODULO % i].x * (MODULO - MODULO / i) % MODULO;
    }
    _fact[0] = 1;
    for (unsigned i = 1; i <= TABLE_SIZE; ++i) {
      _fact[i] = _fact[i - 1] * int(i);
    }
    _inv_fact[TABLE_SIZE] = _fact[TABLE_SIZE].inv();
    for (int i = (int)TABLE_SIZE - 1; i >= 0; --i) {
      _inv_fact[i] = _inv_fact[i + 1] * (i + 1);
    }
  }
};
template <int M, unsigned F>
std::ostream &operator<<(std::ostream &os, const mod_int<M, F> &rhs) {
  return os << rhs.x;
}
template <int M, unsigned F>
std::istream &operator>>(std::istream &is, mod_int<M, F> &rhs) {
  long long s;
  is >> s;
  rhs = mod_int<M, F>(s);
  return is;
}
template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv[TABLE_SIZE + 1];
template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_fact[TABLE_SIZE + 1];
template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv_fact[TABLE_SIZE + 1];
template <int M, unsigned F>
bool operator==(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return lhs.x == rhs.x;
}
template <int M, unsigned F>
bool operator!=(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return !(lhs == rhs);
}
const int MF = 1000010;
const int MOD = 1000000007;
using mint = mod_int<MOD, MF>;
mint binom(int n, int r) {
  return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r);
}
mint fact(int n) { return mint(n).fact(); }
mint inv_fact(int n) { return mint(n).inv_fact(); }
signed main() {
  long long t;
  cin >> t;
  for (long long z = 0; z < (long long)(t); z++) {
    long long x;
    cin >> x;
    bool check = true;
    for (long long n = 300000; n >= 1; n--) {
      long long nm = n * n - x;
      long long sm = sqrt(nm);
      if (sm * sm != nm) continue;
      if (sm == 0) continue;
      long long m = n / sm;
      if (n / m != sm) continue;
      if (m <= n) {
        check = false;
        cout << n << " " << m << endl;
        break;
      }
    }
    if (check) cout << -1 << endl;
  }
  return 0;
}

### Prompt

Generate a cpp solution to the following problem:

Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero. 

Consider the following problem:

You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.

You don't have to solve this problem. Instead, you have to construct a few tests for it.

You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.

Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).

Note that in hacks you have to set t = 1.

Output

For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer  - 1. 

Example

Input

3
21
0
1


Output

5 2
1 1
-1

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
double PI = acos(-1);
namespace {
template <typename T>
std::ostream &operator<<(std::ostream &, const std::vector<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::deque<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::set<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::stack<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::queue<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::priority_queue<T> &);
template <typename T>
std::ostream &operator<<(std::ostream &, const std::unordered_set<T> &);
template <typename T, typename U>
std::ostream &operator<<(std::ostream &, const std::map<T, U> &);
template <typename T, typename U>
std::ostream &operator<<(std::ostream &, const std::unordered_map<T, U> &);
template <typename T, typename U>
std::ostream &operator<<(std::ostream &, const std::pair<T, U> &);
template <typename... T>
std::ostream &operator<<(std::ostream &, const std::tuple<T...> &);
template <typename T, std::size_t N>
std::ostream &operator<<(std::ostream &, const std::array<T, N> &);
template <typename Tuple, std::size_t N>
struct __TuplePrinter__ {
  static void print(std::ostream &os, const Tuple &t) {
    __TuplePrinter__<Tuple, N - 1>::print(os, t);
    os << ", " << std::get<N - 1>(t);
  }
};
template <typename Tuple>
struct __TuplePrinter__<Tuple, 1> {
  static void print(std::ostream &os, const Tuple &t) { os << std::get<0>(t); }
};
template <typename... T>
std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) {
  os << '(';
  __TuplePrinter__<decltype(t), sizeof...(T)>::print(os, t);
  os << ')';
  return os;
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &v) {
  return os << '(' << v.first << ", " << v.second << ')';
}
template <typename T, std::size_t N>
std::ostream &operator<<(std::ostream &os, const std::array<T, N> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::deque<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::set<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::stack<T> &c) {
  std::deque<T> v;
  for (auto d = c; !d.empty(); d.pop()) v.push_front(d.top());
  return os << v;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::queue<T> &c) {
  std::deque<T> v;
  for (auto d = c; !d.empty(); d.pop()) v.push_back(d.front());
  return os << v;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::priority_queue<T> &c) {
  std::deque<T> v;
  for (auto d = c; !d.empty(); d.pop()) v.push_front(d.top());
  return os << v;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::unordered_set<T> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::map<T, U> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::unordered_map<T, U> &c) {
  os << '[';
  for (auto it = begin(c); it != end(c);) {
    os << *it;
    os << (++it != end(c) ? ", " : "");
  }
  return os << ']';
}
}  // namespace
template <signed M, unsigned T>
struct mod_int {
  constexpr static signed MODULO = M;
  constexpr static unsigned TABLE_SIZE = T;
  signed x;
  mod_int() : x(0) {}
  mod_int(long long y)
      : x(static_cast<signed>(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) {}
  mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) {}
  mod_int &operator+=(const mod_int &rhs) {
    if ((x += rhs.x) >= MODULO) x -= MODULO;
    return *this;
  }
  mod_int &operator-=(const mod_int &rhs) {
    if ((x += MODULO - rhs.x) >= MODULO) x -= MODULO;
    return *this;
  }
  mod_int &operator*=(const mod_int &rhs) {
    x = static_cast<signed>(1LL * x * rhs.x % MODULO);
    return *this;
  }
  mod_int &operator/=(const mod_int &rhs) {
    x = static_cast<signed>((1LL * x * rhs.inv().x) % MODULO);
    return *this;
  }
  mod_int operator-() const { return mod_int(-x); }
  mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; }
  mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; }
  mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; }
  mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; }
  bool operator<(const mod_int &rhs) const { return x < rhs.x; }
  mod_int inv() const {
    assert(x != 0);
    if (x <= static_cast<signed>(TABLE_SIZE)) {
      if (_inv[1].x == 0) prepare();
      return _inv[x];
    } else {
      signed a = x, b = MODULO, u = 1, v = 0, t;
      while (b) {
        t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }
      return mod_int(u);
    }
  }
  mod_int pow(long long t) const {
    assert(!(x == 0 && t == 0));
    mod_int e = *this, res = mod_int(1);
    for (; t; e *= e, t >>= 1)
      if (t & 1) res *= e;
    return res;
  }
  mod_int fact() {
    if (_fact[0].x == 0) prepare();
    return _fact[x];
  }
  mod_int inv_fact() {
    if (_fact[0].x == 0) prepare();
    return _inv_fact[x];
  }
  mod_int choose(mod_int y) {
    assert(y.x <= x);
    return this->fact() * y.inv_fact() * mod_int(x - y.x).inv_fact();
  }
  static mod_int _inv[TABLE_SIZE + 1];
  static mod_int _fact[TABLE_SIZE + 1];
  static mod_int _inv_fact[TABLE_SIZE + 1];
  static void prepare() {
    _inv[1] = 1;
    for (int i = 2; i <= (int)TABLE_SIZE; ++i) {
      _inv[i] = 1LL * _inv[MODULO % i].x * (MODULO - MODULO / i) % MODULO;
    }
    _fact[0] = 1;
    for (unsigned i = 1; i <= TABLE_SIZE; ++i) {
      _fact[i] = _fact[i - 1] * int(i);
    }
    _inv_fact[TABLE_SIZE] = _fact[TABLE_SIZE].inv();
    for (int i = (int)TABLE_SIZE - 1; i >= 0; --i) {
      _inv_fact[i] = _inv_fact[i + 1] * (i + 1);
    }
  }
};
template <int M, unsigned F>
std::ostream &operator<<(std::ostream &os, const mod_int<M, F> &rhs) {
  return os << rhs.x;
}
template <int M, unsigned F>
std::istream &operator>>(std::istream &is, mod_int<M, F> &rhs) {
  long long s;
  is >> s;
  rhs = mod_int<M, F>(s);
  return is;
}
template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv[TABLE_SIZE + 1];
template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_fact[TABLE_SIZE + 1];
template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv_fact[TABLE_SIZE + 1];
template <int M, unsigned F>
bool operator==(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return lhs.x == rhs.x;
}
template <int M, unsigned F>
bool operator!=(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
  return !(lhs == rhs);
}
const int MF = 1000010;
const int MOD = 1000000007;
using mint = mod_int<MOD, MF>;
mint binom(int n, int r) {
  return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r);
}
mint fact(int n) { return mint(n).fact(); }
mint inv_fact(int n) { return mint(n).inv_fact(); }
signed main() {
  long long t;
  cin >> t;
  for (long long z = 0; z < (long long)(t); z++) {
    long long x;
    cin >> x;
    bool check = true;
    for (long long n = 300000; n >= 1; n--) {
      long long nm = n * n - x;
      long long sm = sqrt(nm);
      if (sm * sm != nm) continue;
      if (sm == 0) continue;
      long long m = n / sm;
      if (n / m != sm) continue;
      if (m <= n) {
        check = false;
        cout << n << " " << m << endl;
        break;
      }
    }
    if (check) cout << -1 << endl;
  }
  return 0;
}

```