#include <bits/stdc++.h>
using namespace std;
template <class T>
T max(T a, T b, T c) {
  return max(a, max(b, c));
}
template <class T>
T min(T a, T b, T c) {
  return min(a, min(b, c));
}
void fastio() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
bool prime[100005];
void SieveOfEratosthenes(long long int n) {
  memset(prime, true, sizeof(prime));
  for (long long int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (long long int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
}
bool isPrime(long long int n) {
  if (n < 2) return false;
  for (long long int i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
std::vector<long long int> generatePrimeFactors(long long int n) {
  std::vector<long long int> prime;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      prime.push_back(i);
      while (n % i == 0) n = n / i;
    }
  }
  if (n != 1) prime.push_back(n);
  return prime;
}
std::vector<long long int> generateFactors(long long int n) {
  std::vector<long long int> fact;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      fact.push_back(i);
      if (n / i != i) fact.push_back(n / i);
    }
  }
  fact.push_back(1);
  fact.push_back(n);
  sort(fact.begin(), fact.end());
  return fact;
}
long long int gcd(long long int a, long long int b) {
  if (!b) return a;
  return gcd(b, a % b);
}
long long int modpow(long long int x, long long int n, long long int m) {
  if (n == 0) return 1 % m;
  long long int u = modpow(x, n / 2, m) % m;
  u = ((u % m) * (u % m)) % m;
  if (n % 2 == 1) u = ((u % m) * (x % m)) % m;
  return u % m;
}
long long int eulerstotientfunction(long long int n) {
  long long int ans = n;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      while (n % i == 0) n = n / i;
      ans -= ans / i;
    }
  }
  if (n > 1) ans -= ans / n;
  return ans;
}
long long int modinverse(long long int x, long long int m) {
  return modpow(x, m - 2, m);
}
long long int add(long long int a, long long int b, long long int m) {
  return (((a % m) + (b % m)) % m);
}
long long int substract(long long int a, long long int b, long long int m) {
  return (((a % m) - (b % m) + m) % m);
}
long long int multiply(long long int a, long long int b, long long int m) {
  return (((a % m) * (b % m)) % m);
}
long long int divide(long long int a, long long int b, long long int m) {
  long long int temp = modinverse(b, m);
  return multiply(a, temp, m);
}
long long int singlemod(long long int a, long long int m) { return (a % m); }
long long int ncr(long long int n, long long int k, long long int m) {
  if (k > n) return 0;
  long long int res = 1;
  k = min(k, n - k);
  for (long long int i = 1; i <= k; i++) {
    res = multiply(res, n - i + 1, m);
    res = divide(res, i, m);
  }
  return singlemod(res, m);
}
long long int kadaneAlgo(const std::vector<long long int> &arr) {
  long long int size = arr.size();
  long long int currmax = arr[0], maxsofar = arr[0];
  for (long long int i = 1; i < size; i++) {
    currmax = max(arr[i], currmax + arr[i]);
    maxsofar = max(maxsofar, currmax);
  }
  return maxsofar;
}
long long int getDigitSum(long long int n) {
  long long int co = 0;
  while (n > 0) {
    co += n % 10;
    n = n / 10;
  }
  return co;
}
template <class T>
void printVector(const std::vector<T> arr) {
  for (auto i : arr) cout << i << " ";
  cout << '\n';
}
template <class T>
void printArray(T arr[], long long int n) {
  for (long long int i = 1; i <= n; i++) cout << arr[i] << " ";
  cout << '\n';
}
long long int solve(long long int pos, string str, long long int final,
                    long long int curr) {
  if (pos == str.length()) return curr == final;
  if (str[pos] == '+')
    return solve(pos + 1, str, final, curr + 1);
  else if (str[pos] == '-')
    return solve(pos + 1, str, final, curr - 1);
  else {
    return (solve(pos + 1, str, final, curr + 1) +
            solve(pos + 1, str, final, curr - 1));
  }
}
int main() {
  fastio();
  long long int t = 1;
  while (t--) {
    long long int n, m, ans = 0;
    cin >> n >> m;
    for (long long int i = 0; i <= min(n, m); i++) {
      long long int a = n - i, b = m - i;
      ans = max(ans, min(i, a + b));
    }
    cout << ans << '\n';
  }
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

A and B are preparing themselves for programming contests.

An important part of preparing for a competition is sharing programming knowledge from the experienced members to those who are just beginning to deal with the contests. Therefore, during the next team training A decided to make teams so that newbies are solving problems together with experienced participants.

A believes that the optimal team of three people should consist of one experienced participant and two newbies. Thus, each experienced participant can share the experience with a large number of people.

However, B believes that the optimal team should have two experienced members plus one newbie. Thus, each newbie can gain more knowledge and experience.

As a result, A and B have decided that all the teams during the training session should belong to one of the two types described above. Furthermore, they agree that the total number of teams should be as much as possible.

There are n experienced members and m newbies on the training session. Can you calculate what maximum number of teams can be formed?

Input

The first line contains two integers n and m (0 ≤ n, m ≤ 5·105) — the number of experienced participants and newbies that are present at the training session. 

Output

Print the maximum number of teams that can be formed.

Examples

Input

2 6


Output

2


Input

4 5


Output

3

Note

Let's represent the experienced players as XP and newbies as NB.

In the first test the teams look as follows: (XP, NB, NB), (XP, NB, NB).

In the second test sample the teams look as follows: (XP, NB, NB), (XP, NB, NB), (XP, XP, NB).

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
T max(T a, T b, T c) {
  return max(a, max(b, c));
}
template <class T>
T min(T a, T b, T c) {
  return min(a, min(b, c));
}
void fastio() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
bool prime[100005];
void SieveOfEratosthenes(long long int n) {
  memset(prime, true, sizeof(prime));
  for (long long int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (long long int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
}
bool isPrime(long long int n) {
  if (n < 2) return false;
  for (long long int i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
std::vector<long long int> generatePrimeFactors(long long int n) {
  std::vector<long long int> prime;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      prime.push_back(i);
      while (n % i == 0) n = n / i;
    }
  }
  if (n != 1) prime.push_back(n);
  return prime;
}
std::vector<long long int> generateFactors(long long int n) {
  std::vector<long long int> fact;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      fact.push_back(i);
      if (n / i != i) fact.push_back(n / i);
    }
  }
  fact.push_back(1);
  fact.push_back(n);
  sort(fact.begin(), fact.end());
  return fact;
}
long long int gcd(long long int a, long long int b) {
  if (!b) return a;
  return gcd(b, a % b);
}
long long int modpow(long long int x, long long int n, long long int m) {
  if (n == 0) return 1 % m;
  long long int u = modpow(x, n / 2, m) % m;
  u = ((u % m) * (u % m)) % m;
  if (n % 2 == 1) u = ((u % m) * (x % m)) % m;
  return u % m;
}
long long int eulerstotientfunction(long long int n) {
  long long int ans = n;
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      while (n % i == 0) n = n / i;
      ans -= ans / i;
    }
  }
  if (n > 1) ans -= ans / n;
  return ans;
}
long long int modinverse(long long int x, long long int m) {
  return modpow(x, m - 2, m);
}
long long int add(long long int a, long long int b, long long int m) {
  return (((a % m) + (b % m)) % m);
}
long long int substract(long long int a, long long int b, long long int m) {
  return (((a % m) - (b % m) + m) % m);
}
long long int multiply(long long int a, long long int b, long long int m) {
  return (((a % m) * (b % m)) % m);
}
long long int divide(long long int a, long long int b, long long int m) {
  long long int temp = modinverse(b, m);
  return multiply(a, temp, m);
}
long long int singlemod(long long int a, long long int m) { return (a % m); }
long long int ncr(long long int n, long long int k, long long int m) {
  if (k > n) return 0;
  long long int res = 1;
  k = min(k, n - k);
  for (long long int i = 1; i <= k; i++) {
    res = multiply(res, n - i + 1, m);
    res = divide(res, i, m);
  }
  return singlemod(res, m);
}
long long int kadaneAlgo(const std::vector<long long int> &arr) {
  long long int size = arr.size();
  long long int currmax = arr[0], maxsofar = arr[0];
  for (long long int i = 1; i < size; i++) {
    currmax = max(arr[i], currmax + arr[i]);
    maxsofar = max(maxsofar, currmax);
  }
  return maxsofar;
}
long long int getDigitSum(long long int n) {
  long long int co = 0;
  while (n > 0) {
    co += n % 10;
    n = n / 10;
  }
  return co;
}
template <class T>
void printVector(const std::vector<T> arr) {
  for (auto i : arr) cout << i << " ";
  cout << '\n';
}
template <class T>
void printArray(T arr[], long long int n) {
  for (long long int i = 1; i <= n; i++) cout << arr[i] << " ";
  cout << '\n';
}
long long int solve(long long int pos, string str, long long int final,
                    long long int curr) {
  if (pos == str.length()) return curr == final;
  if (str[pos] == '+')
    return solve(pos + 1, str, final, curr + 1);
  else if (str[pos] == '-')
    return solve(pos + 1, str, final, curr - 1);
  else {
    return (solve(pos + 1, str, final, curr + 1) +
            solve(pos + 1, str, final, curr - 1));
  }
}
int main() {
  fastio();
  long long int t = 1;
  while (t--) {
    long long int n, m, ans = 0;
    cin >> n >> m;
    for (long long int i = 0; i <= min(n, m); i++) {
      long long int a = n - i, b = m - i;
      ans = max(ans, min(i, a + b));
    }
    cout << ans << '\n';
  }
}

```