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;
inline char skipwhitespace() {
  char ch = getchar();
  while (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t') ch = getchar();
  return ch;
}
void gi(int &x) {
  register int c = getchar();
  x = 0;
  int sn = 1;
  for (; (c < 48 || c > 57); c = getchar())
    if (c == '-') sn = -1;
  for (; c > 47 && c < 58; c = getchar()) {
    x = (x << 1) + (x << 3) + c - 48;
  }
  x *= sn;
}
void gii(long long int &x) {
  register long long int c = getchar();
  x = 0;
  long long int sn = 1;
  for (; (c < 48 || c > 57); c = getchar())
    if (c == '-') sn = -1;
  for (; c > 47 && c < 58; c = getchar()) {
    x = (x << 1) + (x << 3) + c - 48;
  }
  x *= sn;
}
void wi(int n) {
  int sign = n >= 0 ? 1 : -1;
  n = n > 0 ? n : -n;
  char buf[10];
  int i = 9;
  if (!n) buf[i--] = 48;
  while (n) {
    buf[i--] = n % 10 + 48;
    n /= 10;
  }
  if (sign < 0) printf("%c", '-');
  while (++i < 10) printf("%c", buf[i]);
}
void wii(long long int n) {
  long long int sign = n >= 0 ? 1 : -1;
  n = n > 0 ? n : -n;
  char buf[25];
  long long int i = 24;
  if (!n) buf[i--] = 48;
  while (n) {
    buf[i--] = n % 10 + 48;
    n /= 10;
  }
  if (sign < 0) printf("%c", '-');
  while (++i < 25) printf("%c", buf[i]);
}
int gs(char *s) {
  char ch = skipwhitespace();
  int n = 0;
  while ((ch != '\n' && ch != ' ' && ch != '\t')) {
    s[n++] = ch;
    ch = getchar();
  }
  s[n] = 0;
  return n;
}
void ws(char *s) {
  char *p = s;
  while (*p) {
    printf("%c", *p);
    p++;
  }
}
int main() {
  double n, m;
  scanf("%lf%lf", &n, &m);
  if (m == n && m == 1) {
    cout << "1" << endl;
    return 0;
  }
  printf("%.10lf\n", (1 / n) + ((n - 1) / n) * ((m - 1) / (m * n - 1)));
  return 0;
}