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;
ifstream fin("A.in");
ofstream fout("A.out");
long double dp[1002][1002], ans;
int n, m;
int main() {
  cin >> n >> m;
  dp[0][0] = 1;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j <= min(n, m); ++j) {
      if (dp[i][j] > 1e-12) {
        dp[i + 1][j + 1] += dp[i][j] * (m - j) / (n * m - i);
        dp[i + 1][j] += dp[i][j] * ((n - 1) * m - (i - j)) / (n * m - i);
      }
    }
  }
  for (int j = 1; j <= m; ++j) {
    ans += dp[n][j] * j * j / n;
  }
  cout << fixed << setprecision(7) << ans;
}