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;
template <class T>
T gcd(T a, T b) {
  T r;
  while (b != 0) {
    r = a % b;
    a = b;
    b = r;
  }
  return a;
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
template <class T>
int getbit(T s, int i) {
  return (s >> i) & 1;
}
template <class T>
T onbit(T s, int i) {
  return s | (T(1) << i);
}
template <class T>
T offbit(T s, int i) {
  return s & (~(T(1) << i));
}
const double PI = 2 * acos(0.0);
const double eps = 1e-9;
const int infi = 1e9;
const long long Linfi = (long long)1e18;
const long long MOD = 1000000000;
long long c1 = 3137;
int n, m;
double F[1005][1005];
void solve() {
  F[1][1] = 1;
  int total = n * m;
  for (int i = 2; i <= n; i++)
    for (int j = 1; j <= i; j++) {
      F[j][i] = F[j - 1][i - 1] * (m - j + 1) / (total - i + 1);
      F[j][i] += F[j][i - 1] * (total - i + 1 - m + j) / (total - i + 1);
    }
  double ans = 0;
  for (int j = 1; j <= m; j++) ans += F[j][n] * j / n;
  printf("%.6lf\n", ans);
}
int main() {
  cin >> n >> m;
  solve();
  return 0;
}