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>
#pragma comment(linker, "/STACK:500000000")
using namespace std;
double C[1009][1009];
vector<int> A, B;
void add(int n, int k, vector<int> &A, vector<int> &B) {
  for (int i = 0; i < k; i++) B.push_back(k - i), A.push_back(n - i);
}
int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  double res = 0;
  for (int k = 0; k <= n; k++) {
    A.clear(), B.clear();
    add(m, k, A, B);
    add(n * m - m, n - k, A, B);
    add(n * m, n, B, A);
    sort(A.begin(), A.end());
    sort(B.begin(), B.end());
    double ml = 1.0 * k * k / n / n;
    for (int i = 0; i < A.size(); i++) ml *= 1.0 * A[i] / B[i];
    res += ml;
  }
  printf("%.13f\n", n * res);
}