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 N, M;
double logF[1000 * 1000 + 1];
double log_mCn(int m, int n) { return logF[m] - logF[n] - logF[m - n]; }
int main() {
  cin.sync_with_stdio(false);
  cin >> N >> M;
  logF[0] = 0.0;
  for (int i = 1; i <= N * M; ++i) logF[i] = log((double)i) + logF[i - 1];
  double ans = 0.0;
  for (int i = 1; i <= min(M, N); ++i) {
    double x = (double)i / (double)N;
    double y = log_mCn(M, i) + log_mCn(M * (N - 1), N - i) - log_mCn(M * N, N);
    ans += exp(y) * x * x;
  }
  ans *= N;
  cout << setprecision(10) << fixed << ans << endl;
  return 0;
}