Problem: Alex enjoys performing magic tricks. He has a trick that requires a deck of n cards. He has m identical decks of n different cards each, which have been mixed together. When Alex wishes to perform the trick, he grabs n cards at random and performs the trick with those. The resulting deck looks like a normal deck, but may have duplicates of some cards.

The trick itself is performed as follows: first Alex allows you to choose a random card from the deck. You memorize the card and put it back in the deck. Then Alex shuffles the deck, and pulls out a card. If the card matches the one you memorized, the trick is successful.

You don't think Alex is a very good magician, and that he just pulls a card randomly from the deck. Determine the probability of the trick being successful if this is the case.

Input

First line of the input consists of two integers n and m (1 ≤ n, m ≤ 1000), separated by space — number of cards in each deck, and number of decks.

Output

On the only line of the output print one floating point number – probability of Alex successfully performing the trick. Relative or absolute error of your answer should not be higher than 10 - 6.

Examples

Input

2 2


Output

0.6666666666666666


Input

4 4


Output

0.4000000000000000


Input

1 2


Output

1.0000000000000000

Note

In the first sample, with probability <image> Alex will perform the trick with two cards with the same value from two different decks. In this case the trick is guaranteed to succeed.

With the remaining <image> probability he took two different cards, and the probability of pulling off the trick is <image>.

The resulting probability is <image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
template <class T>
typename T::value_type arr_sum(const T& v, int n) {
  typename T::value_type sum = 0;
  for (int i = 0; i < n; ++i) sum += v[i];
  return sum;
}
template <class T>
long long arr_count(const T& v, int n, int t) {
  long long count = 0;
  for (int i = 0; i < n; ++i) count += (v[i] == t);
  return count;
}
template <class T>
typename T::value_type arr_maxi(const T& v, int n) {
  typename T::value_type maxi = 0;
  for (int i = 1; i < n; ++i)
    if (v[maxi] < v[i]) maxi = i;
  return maxi;
}
template <class T>
typename T::value_type arr_mini(const T& v, int n) {
  typename T::value_type mini = 0;
  for (int i = 1; i < n; ++i)
    if (v[mini] > v[i]) mini = i;
  return mini;
}
template <class T>
typename T::value_type arr_max(const T& v, int n) {
  typename T::value_type max = v[0];
  for (int i = 1; i < n; ++i)
    if (max < v[i]) max = v[i];
  return max;
}
template <class T>
typename T::value_type arr_min(const T& v, int n) {
  typename T::value_type min = v[0];
  for (int i = 1; i < n; ++i)
    if (min > v[i]) min = v[i];
  return min;
}
using namespace std;
int main() {
  long double n, m;
  cin >> n >> m;
  if (n == 1 && m == 1) {
    cout << 1.0 << endl;
    return 0;
  }
  cout << fixed << setprecision(10)
       << 1 / n + (n - 1) * (m - 1) / n / (n * m - 1) << endl;
  return 0;
}