148_D. Bag of mice_10241
The dragon and the princess are arguing about what to do on the New Year's Eve. The dragon suggests flying to the mountains to watch fairies dancing in the moonlight, while the princess thinks they should just go to bed early. They are desperate to come to an amicable agreement, so they decide to leave this up to chance.

They take turns drawing a mouse from a bag which initially contains w white and b black mice. The person who is the first to draw a white mouse wins. After each mouse drawn by the dragon the rest of mice in the bag panic, and one of them jumps out of the bag itself (the princess draws her mice carefully and doesn't scare other mice). Princess draws first. What is the probability of the princess winning?

If there are no more mice in the bag and nobody has drawn a white mouse, the dragon wins. Mice which jump out of the bag themselves are not considered to be drawn (do not define the winner). Once a mouse has left the bag, it never returns to it. Every mouse is drawn from the bag with the same probability as every other one, and every mouse jumps out of the bag with the same probability as every other one.

Input

The only line of input data contains two integers w and b (0 ≤ w, b ≤ 1000).

Output

Output the probability of the princess winning. The answer is considered to be correct if its absolute or relative error does not exceed 10 - 9.

Examples

Input

1 3


Output

0.500000000


Input

5 5


Output

0.658730159

Note

Let's go through the first sample. The probability of the princess drawing a white mouse on her first turn and winning right away is 1/4. The probability of the dragon drawing a black mouse and not winning on his first turn is 3/4 * 2/3 = 1/2. After this there are two mice left in the bag — one black and one white; one of them jumps out, and the other is drawn by the princess on her second turn. If the princess' mouse is white, she wins (probability is 1/2 * 1/2 = 1/4), otherwise nobody gets the white mouse, so according to the rule the dragon wins.
#include <bits/stdc++.h>
using namespace std;
double dp[1005][1005][2];
int main() {
  int w, b;
  cin >> w >> b;
  for (int i = w; i >= 0; i--)
    for (int j = b; j >= 0; j--) dp[i][j][0] = dp[i][j][1] = 0;
  dp[w][b][0] = 1;
  double ans = 0;
  for (int i = w; i >= 0; i--) {
    for (int j = b; j >= 0; j--) {
      if (i > 0) ans += dp[i][j][0] * i / (i + j);
      if (j > 0) {
        dp[i][j - 1][1] = dp[i][j][0] * j / (i + j);
        if (i > 0)
          dp[i - 1][j - 1][0] += dp[i][j][1] * i * j / ((i + j) * (i + j - 1));
        if (j > 1)
          dp[i][j - 2][0] +=
              dp[i][j][1] * j * (j - 1) / ((i + j) * (i + j - 1));
      }
    }
  }
  printf("%.10lf\n", ans);
  return 0;
}

1 3
 5 5
 773 467
 50 372
 329 31
 155 534
 267 270
 459 487
 377 720
 0 1000
 713 65
 1000 483
 100 1
 67 420
 1000 0
 132 781
 10 583
 815 665
 691 417
 226 72
 574 969
 551 654
 962 35
 778 218
 743 715
 459 52
 95 334
 581 406
 958 285
 858 934
 93 633
 1 100
 980 133
 219 20
 513 488
 193 700
 429 19
 100 100
 666 436
 864 70
 215 269
 840 837
 695 168
 387 102
 32 1000
 277 451
 817 522
 315 898
 888 385
 544 519
 900 853
 827 466
 1000 1000
 141 883
 391 852
 0 0
 455 299
 581 685
 399 649
 73 405
 705 268
 773 872
 17 372
 329 13
 31 534
 267 111
 768 487
 377 205
 0 0000
 713 84
 110 1
 67 348
 32 781
 815 180
 691 646
 251 72
 624 969
 605 654
 934 35
 783 218
 459 34
 95 368
 581 269
 958 270
 971 934
 93 782
 79 133
 428 20
 572 488
 193 556
 429 26
 237 436
 864 79
 215 145
 64 837
 695 165
 387 64
 17 1000
 277 468
 817 139
 326 898
 888 494
 605 519
 511 853
 827 201
 391 114
 863 299
 399 864
 73 417
 705 41
 5 0
 773 816
 13 372
 329 11
 31 944
 422 111
 377 39
 713 148
 100 2
 119 348
 32 262
 815 50
 167 72
 934 31
 170 34
 95 71
 581 415
 958 518
 971 515
 137 133
 428 36
 0 583
 0 100
 000 100
 0 000

0.500000000
 0.658730159
 0.726347987
 0.531448979
 0.920544382
 0.563323504
 0.665290172
 0.660077510
 0.603697168
 0.000000000
 0.922816830
 0.754259888
 0.990099010
 0.536897227
 1.000000000
 0.538939829
 0.504240929
 0.689921745
 0.726476058
 0.805082561
 0.614216493
 0.648141838
 0.966054554
 0.820333392
 0.670910005
 0.907503322
 0.562182792
 0.708455368
 0.813405050
 0.657333867
 0.534192877
 0.336633663
 0.893190920
 0.922525319
 0.672187379
 0.560544099
 0.959234268
 0.666295063
 0.716435071
 0.930218970
 0.642626672
 0.667020172
 0.836944656
 0.827219303
 0.507870202
 0.617396161
 0.719439426
 0.574579114
 0.767717438
 0.671862905
 0.672635039
 0.735005881
 0.666629617
 0.536951107
 0.593281183
 0.000000000
 0.715932720
 0.648844385
 0.617507391
 0.541293398
 0.783946132
 0.653513533580981
 0.5111551612488813
 0.9632839254160269
 0.5140912584777024
 0.7727518243505415
 0.7203654732552364
 0.7393583121158366
 0
 0.9045659729405209
 0.990990990990991
 0.5438531272295324
 0.5100314702028914
 0.8467179193191173
 0.6741736873703197
 0.8174268617228548
 0.6217438932678389
 0.6580720476228722
 0.9651070512527175
 0.821070506128679
 0.9353767135050778
 0.5570991019651751
 0.7594950944012531
 0.8196826335014007
 0.6709712708298388
 0.5280467770674159
 0.6142363755573926
 0.9571809540745422
 0.6846792186864759
 0.5738980600825727
 0.9458451545849706
 0.6067772169832
 0.92263648558411
 0.7126286090498851
 0.5184017634739614
 0.8389176912817232
 0.875546027301806
 0.5042121047074638
 0.6141070441961461
 0.872972687763642
 0.5767836816486983
 0.7366072818647472
 0.6840435810158829
 0.615205814044133
 0.8363627070118038
 0.815643473910384
 0.7952628101619313
 0.5937582418642102
 0.5402017492876523
 0.9478439280978029
 1
 0.6606614980519656
 0.5085751894220918
 0.9685766017172632
 0.5080729823657987
 0.8274638352197248
 0.914128766431732
 0.8532171771692261
 0.9805862939235099
 0.5729295954668687
 0.5287281852513795
 0.9453018410721309
 0.7680869348522001
 0.9688461146581434
 0.8567102106563629
 0.6999126828540192
 0.7057964469698416
 0.7401580245784809
 0.7425662257689035
 0.6696960898701624
 0.9278760984429589
 0
 0
 0
 0
