#include <bits/stdc++.h>
using namespace std;
const long long int inf = 1e18;
const long long int mod = 1e9 + 7;
const long long int MOD = 998244353;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c *x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug &operator<<(const c &) {
    return *this;
  }
};
vector<char *> tokenizer(const char *args) {
  char *token = new char[111];
  strcpy(token, args);
  token = strtok(token, ", ");
  vector<char *> v({token});
  while ((token = strtok(NULL, ", "))) v.push_back(token);
  return reverse(v.begin(), v.end()), v;
}
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wunused-parameter"
void debugg(vector<char *> args) { cerr << "\b\b "; }
#pragma clang diagnostic pop
template <typename Head, typename... Tail>
void debugg(vector<char *> args, Head H, Tail... T) {
  debug() << " [" << args.back() << ": " << H << "] ";
  args.pop_back();
  debugg(args, T...);
}
template <typename T>
bool asc(pair<T, T> &a, pair<T, T> &b) {
  if (a.first == b.first) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
template <typename T>
bool desc(pair<T, T> &a, pair<T, T> &b) {
  if (a.first == b.first) {
    return a.second > b.second;
  }
  return a.first > b.first;
}
template <typename T>
T power(T a, T b) {
  if (b == 0) return 1;
  if (b == 1)
    return a;
  else {
    T res = (power(a, b / 2));
    if (b % 2) {
      return (res * res * a);
    } else {
      return res * res;
    }
  }
}
template <typename T>
T power(T a, T b, T modulo) {
  if (b == 0) return 1;
  if (b == 1)
    return a;
  else {
    T res = (power(a, b / 2, modulo) % modulo);
    if (b % 2) {
      return ((((res % modulo) * (res % modulo)) % modulo) * (a % modulo)) %
             modulo;
    } else {
      return ((res % modulo) * (res % modulo)) % modulo;
    }
  }
}
template <typename T>
T gcd(T a, T b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}
template <typename T>
void primefactorise(T n, vector<T> &vec) {
  while (n % 2 == 0) {
    vec.emplace_back(2);
    n = n / 2;
  }
  for (int i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      vec.emplace_back(i);
      n = n / i;
    }
  }
  if (n > 2) {
    vec.emplace_back(n);
  }
}
template <typename T>
void all_factor(T n, vector<T> &vec) {
  for (auto i = 1; i <= sqrt(n); ++i) {
    if (n % i == 0) {
      vec.emplace_back(i);
      if (i != (n / i)) {
        vec.emplace_back(n / i);
      }
    }
  }
}
long long mod_inv(long long a) {
  return (power<long long>(a, mod - 2, mod)) % mod;
}
void factorial(vector<long long int> &fact, long long n) {
  fact.resize(n + 1, 1);
  fact[0] = 1;
  fact[1] = 1;
  for (int i = 2; i <= n; ++i) {
    fact[i] = ((fact[i - 1] % mod) * (i % mod)) % mod;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  long long l, s;
  cin >> s >> l;
  vector<long long int> v;
  for (; l >= 1; l--) {
    long long d = l & (-l);
    {};
    if (d <= s) {
      s -= d;
      v.emplace_back(l);
    }
    if (s == 0) {
      break;
    }
  }
  if (s > 0) {
    cout << ((-1)) << "\n";
    ;
    return 0;
  }
  cout << ((v.size())) << "\n";
  ;
  for (auto &item : v) cout << item << " ";
  cout << "\n";
  ;
  {};
  return 0;
}

### Prompt

Please formulate a CPP solution to the following problem:

At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.

Fortunately, Picks remembers something about his set S:

  * its elements were distinct integers from 1 to limit; 
  * the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation). 



Can you help Picks and find any set S, that satisfies all the above conditions?

Input

The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).

Output

In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.

If it's impossible to find a suitable set, print -1.

Examples

Input

5 5


Output

2
4 5


Input

4 3


Output

3
2 3 1


Input

5 1


Output

-1

Note

In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.

In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long int inf = 1e18;
const long long int mod = 1e9 + 7;
const long long int MOD = 998244353;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c *x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug &operator<<(const c &) {
    return *this;
  }
};
vector<char *> tokenizer(const char *args) {
  char *token = new char[111];
  strcpy(token, args);
  token = strtok(token, ", ");
  vector<char *> v({token});
  while ((token = strtok(NULL, ", "))) v.push_back(token);
  return reverse(v.begin(), v.end()), v;
}
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wunused-parameter"
void debugg(vector<char *> args) { cerr << "\b\b "; }
#pragma clang diagnostic pop
template <typename Head, typename... Tail>
void debugg(vector<char *> args, Head H, Tail... T) {
  debug() << " [" << args.back() << ": " << H << "] ";
  args.pop_back();
  debugg(args, T...);
}
template <typename T>
bool asc(pair<T, T> &a, pair<T, T> &b) {
  if (a.first == b.first) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
template <typename T>
bool desc(pair<T, T> &a, pair<T, T> &b) {
  if (a.first == b.first) {
    return a.second > b.second;
  }
  return a.first > b.first;
}
template <typename T>
T power(T a, T b) {
  if (b == 0) return 1;
  if (b == 1)
    return a;
  else {
    T res = (power(a, b / 2));
    if (b % 2) {
      return (res * res * a);
    } else {
      return res * res;
    }
  }
}
template <typename T>
T power(T a, T b, T modulo) {
  if (b == 0) return 1;
  if (b == 1)
    return a;
  else {
    T res = (power(a, b / 2, modulo) % modulo);
    if (b % 2) {
      return ((((res % modulo) * (res % modulo)) % modulo) * (a % modulo)) %
             modulo;
    } else {
      return ((res % modulo) * (res % modulo)) % modulo;
    }
  }
}
template <typename T>
T gcd(T a, T b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}
template <typename T>
void primefactorise(T n, vector<T> &vec) {
  while (n % 2 == 0) {
    vec.emplace_back(2);
    n = n / 2;
  }
  for (int i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      vec.emplace_back(i);
      n = n / i;
    }
  }
  if (n > 2) {
    vec.emplace_back(n);
  }
}
template <typename T>
void all_factor(T n, vector<T> &vec) {
  for (auto i = 1; i <= sqrt(n); ++i) {
    if (n % i == 0) {
      vec.emplace_back(i);
      if (i != (n / i)) {
        vec.emplace_back(n / i);
      }
    }
  }
}
long long mod_inv(long long a) {
  return (power<long long>(a, mod - 2, mod)) % mod;
}
void factorial(vector<long long int> &fact, long long n) {
  fact.resize(n + 1, 1);
  fact[0] = 1;
  fact[1] = 1;
  for (int i = 2; i <= n; ++i) {
    fact[i] = ((fact[i - 1] % mod) * (i % mod)) % mod;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  long long l, s;
  cin >> s >> l;
  vector<long long int> v;
  for (; l >= 1; l--) {
    long long d = l & (-l);
    {};
    if (d <= s) {
      s -= d;
      v.emplace_back(l);
    }
    if (s == 0) {
      break;
    }
  }
  if (s > 0) {
    cout << ((-1)) << "\n";
    ;
    return 0;
  }
  cout << ((v.size())) << "\n";
  ;
  for (auto &item : v) cout << item << " ";
  cout << "\n";
  ;
  {};
  return 0;
}

```