Kundu has a Bubble Wrap and like all of us she likes popping it. The Bubble wrap has dimensions NxM, i.e. it has N rows and each row has M cells which has a bubble. Initially all bubbles in filled with air and can be popped.
What Kundu does is randomly picks one cell and tries to pop it, there might be a case that the bubble Kundu selected is already popped. In that case he has to ignore this. Both of these steps take 1 second of time. Tell the total expected number of seconds in which Kundu would be able to pop them all.
Input contains a single line containing two space seperated integers, N M, representing the dimension of Bubble wrap.
Output the required answer in one line. The answer will be considered correct, if its absolute error doesn't exceed 10-2.
1 ≤ N, M ≤ 1000
Sample Input #00
Sample Output #00
Sample Input #01
Sample Output #01
Sample Input #02
Sample Output #02
Explanation Test Case #00: There is only one bubble, so he needs only one chance to pop it. Test Case #01: Expected number of steps of popping two bubbles is 3. Test Case #02: There are 4 bubbles with equal probability of popping out. Expected number of steps to pop all of them is 8.333333...