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>
const int N = (int)1e5 + 123;
const double eps = 1e-6;
const int inf = (int)1e9 + 123;
template <class T = int>
inline T readInt();
template <class T = long long>
inline T readLL();
using namespace std;
int n, m;
double res;
int main() {
  n = readInt();
  m = readInt();
  if (n == 1 && m == n) {
    cout << "1";
    return 0;
  }
  res = 1.0 / n;
  res += (1.0 * (n - 1) / n) * (1.0 * (m - 1) / (1.0 * n * m - 1));
  printf("%.10f", res);
  return 0;
}
static const int buf_size = 4096;
inline int getchar_fast() {
  static char buf[buf_size];
  static int len = 0, pos = 0;
  if (pos == len) pos = 0, len = fread(buf, 1, buf_size, stdin);
  if (pos == len) return -1;
  return buf[pos++];
}
inline int readChar() {
  int c = getchar_fast();
  while (c <= 32) c = getchar_fast();
  return c;
}
template <class T>
inline T readInt() {
  int second = 1, c = readChar();
  T x = 0;
  if (c == '-') second = -1, c = getchar_fast();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getchar_fast();
  return second == 1 ? x : -x;
}
template <class T>
inline T readLL() {
  int second = 1, c = readChar();
  T x = 0;
  if (c == '-') second = -1, c = getchar_fast();
  while ('0' <= c && c <= '9') x = x * 10ll + c - '0', c = getchar_fast();
  return second == 1 ? second : -x;
}