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>
using namespace std;
int countBits(long long mask) {
  int res = 0;
  while (mask) mask &= (mask - 1), ++res;
  return res;
}
string toString(long long n) {
  stringstream ss;
  ss << n;
  return ss.str();
}
long long toNumber(string s) {
  stringstream ss;
  long long n;
  ss << s;
  ss >> n;
  return n;
}
void nCr(int n, int k, vector<long double> &foo2, vector<long double> &ta7t) {
  for (int i = (int)(1), _m = (int)(k + 1); i < _m; ++i) ta7t.push_back(i);
  for (int i = (int)(n), _m = (int)(n - k + 1); i >= _m; --i) foo2.push_back(i);
}
long double solve(int n, int m, int m2) {
  vector<long double> foo2, ta7t;
  nCr(n * m - m, n - m2, foo2, ta7t);
  nCr(n * m, n, ta7t, foo2);
  nCr(m, m2, foo2, ta7t);
  foo2.push_back(m2), foo2.push_back(m2);
  ta7t.push_back(n);
  sort(foo2.rbegin(), foo2.rend()), sort(ta7t.rbegin(), ta7t.rend());
  int common = min((int)foo2.size(), (int)ta7t.size());
  long double res = 1;
  for (int i = (int)(0), _m = (int)(common); i < _m; ++i)
    res *= foo2[i] / ta7t[i];
  for (int i = (int)(common), _m = (int)(foo2.size()); i < _m; ++i)
    res *= foo2[i];
  for (int i = (int)(common), _m = (int)(ta7t.size()); i < _m; ++i)
    res /= ta7t[i];
  return res;
}
int main() {
  int n, m;
  while (cin >> n >> m) {
    long double res = 0;
    for (int m2 = (int)(1), _m = (int)(min(n, m) + 1); m2 < _m; ++m2)
      res += solve(n, m, m2);
    cout.precision(8);
    cout << fixed << res << endl;
  }
  return 0;
}