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>
void dbg(const char* fmt, ...) {}
double fact[100];
double c(int n, int k) {
  if (k < 0 || n < k) return 0;
  return fact[n] / fact[k] / fact[n - k];
}
long long gcd(long long a, long long b) { return a ? gcd(b % a, a) : b; }
std::pair<int, int> ans[100][100];
double solve(int n, int m) {
  double count = 0;
  double total_count = 0;
  for (int i = 1; i <= n; i++) {
    double temp = c(m - 1, i - 1) * c(m * (n - 1), n - i);
    total_count += temp;
    count += temp * i / n;
  }
  ans[n][m] =
      std::pair<int, int>((int)round(count * n), (int)round(total_count * n));
  return count / total_count;
}
double solve2(int n, int m) {
  if (n == 1) return 1;
  double ans = 1 / (double)n;
  double nn = n - 2;
  double magic2 = 2 * nn * nn + 7 * nn + 6;
  double magic1 = nn * nn + nn - 1;
  double magic0 = -2 - 3 * nn - nn * nn;
  for (int i = 1; i < m; i++) {
    double zzz = magic2 * i * i + magic1 * i + magic0;
    ans *= 1 + (n - 1) * (n - 1) / zzz;
  }
  return ans;
}
int main() {
  fact[0] = 1;
  for (int i = 1; i < 100; i++) fact[i] = fact[i - 1] * i;
  int n, m;
  scanf("%d%d", &n, &m);
  printf("%.10lf\n", solve2(n, m));
  return 0;
}