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;
long long rdtsc() {
  long long tmp;
  asm("rdtsc" : "=A"(tmp));
  return tmp;
}
inline int myrand() { return abs((rand() << 15) ^ rand()); }
inline int rnd(int x) { return myrand() % x; }
bool solve() {
  int n, m;
  if (scanf("%d%d", &n, &m) < 2) return 0;
  double res = 0;
  double cur = 1;
  for (int i = 0; i < n - 1; ++i)
    cur *= (n * m - m - i + 0.0) / (n * m - 1 - i + 0.0);
  for (int k = 0;; ++k) {
    res += cur * ((double)(k + 1) / n);
    if (k + 1 != n && k + 1 != m) {
      cur *= (m - 1 - k);
      cur /= (k + 1);
      cur *= (n - 1 - k);
      cur /= (n * m - m - n + 1 + k + 1);
    } else
      break;
  }
  printf("%.18lf\n", res);
  return 1;
}
int main() {
  srand(rdtsc());
  while (1) {
    if (!solve()) break;
  }
  return 0;
}