591_A. Wizards' Duel_36761
Harry Potter and He-Who-Must-Not-Be-Named engaged in a fight to the death once again. This time they are located at opposite ends of the corridor of length l. Two opponents simultaneously charge a deadly spell in the enemy. We know that the impulse of Harry's magic spell flies at a speed of p meters per second, and the impulse of You-Know-Who's magic spell flies at a speed of q meters per second.

The impulses are moving through the corridor toward each other, and at the time of the collision they turn round and fly back to those who cast them without changing their original speeds. Then, as soon as the impulse gets back to it's caster, the wizard reflects it and sends again towards the enemy, without changing the original speed of the impulse.

Since Harry has perfectly mastered the basics of magic, he knows that after the second collision both impulses will disappear, and a powerful explosion will occur exactly in the place of their collision. However, the young wizard isn't good at math, so he asks you to calculate the distance from his position to the place of the second meeting of the spell impulses, provided that the opponents do not change positions during the whole fight.

Input

The first line of the input contains a single integer l (1 ≤ l ≤ 1 000) — the length of the corridor where the fight takes place.

The second line contains integer p, the third line contains integer q (1 ≤ p, q ≤ 500) — the speeds of magical impulses for Harry Potter and He-Who-Must-Not-Be-Named, respectively.

Output

Print a single real number — the distance from the end of the corridor, where Harry is located, to the place of the second meeting of the spell impulses. Your answer will be considered correct if its absolute or relative error will not exceed 10 - 4. 

Namely: let's assume that your answer equals a, and the answer of the jury is b. The checker program will consider your answer correct if <image>.

Examples

Input

100
50
50


Output

50


Input

199
60
40


Output

119.4

Note

In the first sample the speeds of the impulses are equal, so both of their meetings occur exactly in the middle of the corridor.
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
	Scanner input = new Scanner(System.in);
	int l = input.nextInt();
	int p = input.nextInt();
	int q = input.nextInt();

	double collisionT = ((double)l)/(p+q);
	double harryDistance = collisionT*p;


	double collisionT2 = ((double)(l*2))/(p+q);
	double harryDistance2 = collisionT2*p;


	double distance = harryDistance2-harryDistance;

	System.out.println(distance);
    }
}
199
60
40
 100
50
50
 978
467
371
 101
11
22
 349
478
378
 600
221
279
 425
458
118
 961
173
47
 961
443
50
 133
53
124
 1000
500
1
 690
499
430
 539
61
56
 496
326
429
 1
500
500
 1
500
1
 678
295
29
 296
467
377
 1000
500
500
 285
468
62
 655
203
18
 745
152
417
 919
323
458
 762
462
371
 253
80
276
 188
59
126
 886
235
95
 1000
1
500
 258
25
431
 623
422
217
 627
150
285
 105
68
403
 987
1
3
 583
112
248
 644
428
484
 1
1
1
 1
1
500
 1000
1
1
 979
39
60
 718
29
375
 903
460
362
 998
224
65
 980
322
193
 871
401
17
 538
479
416
 978
467
133
 349
478
221
 600
356
279
 425
322
118
 961
173
39
 961
782
50
 133
84
124
 1000
792
1
 690
499
106
 539
61
97
 496
326
562
 1
99
500
 1
500
2
 678
295
42
 296
467
313
 1000
90
500
 285
468
123
 655
70
18
 745
70
417
 919
401
458
 762
369
371
 253
56
276
 188
59
118
 886
235
123
 258
25
358
 623
211
217
 627
150
129
 105
61
403
 987
2
3
 583
22
248
 644
83
484
 1
1
397
 1000
2
1
 979
39
54
 718
29
329
 903
460
310
 998
287
65
 980
246
193
 871
401
14
 538
585
416
 199
106
40
 100
50
86
 978
884
133
 349
478
260
 600
356
28
 425
244
118
 961
116
39
 961
556
50
 133
15
124
 1000
792
2
 690
499
56
 539
105
97
 496
622
562
 1
104
500
 678
569
42
 296
467
373
 1000
148
500
 285
446
123
 655
70
35
 745
78
417
 919
393
458
 762
36
371
 253
56
145
 188
45
118
 886
235
241
 258
32
358
 623
211
4
 627
150
107
 105
2
403
 987
2
6
 583
5
248
 644
165
484
 1
1
712
 1000
4
1
 979
39
64
 718
29
451
 903
183
310
 998
188
65
 980
246
238
 871
620
14
 538
585
53
 199
86
40
 100
26
86
 978
884
81
 349
116
260
 600
356
23
 425
244
68
 961
116
18
 961
593
50
 133
15
82
 690
499
79
 539
105
61
 496
622
901
 1
104
205

119.4 50 545.0190930787589
 33.666666666666664
 194.8855140186916
 265.2 337.93402777777777
 755.6954545454546
 863.5354969574037
 39.824858757062145
 998.004 370.6243272335845
 281.017094017094
 214.16688741721853
 0.5 0.998004 617.3148148148148
 163.782 500 251.66037735849056
 601.6515837104073
 199.01581722319858
 380.0729833546735
 422.6218487394958
 56.853932584269664
 59.956756756756754
 630.939393939394
 1.99601 14.144736842105264
 411.433489827856
 216.20689655172413
 15.159235668789808
 246.75 181.37777777777777
 302.2280701754386
 0.5 0.00199601 500 385.6666666666667
 51.5396 505.3284671532847
 773.5363321799308
 612.7378640776699
 835.5765550239234
 287.9351955307263
 761.2099999999999
 238.65808297567955
 336.3779527559055
 311.0227272727273
 784.2122641509434
 903.2475961538461
 53.71153846153846
 998.7389659520808
 569.1074380165289
 208.09493670886076
 182.0900900900901
 0.1652754590984975
 0.9960159362549801
 593.5014836795252
 177.22051282051282
 152.54237288135593
 225.68527918781726
 521.0227272727273
 107.08418891170432
 429.0093131548312
 379.97027027027025
 42.674698795180724
 62.666666666666664
 581.5921787709498
 16.840731070496084
 307.13317757009344
 337.09677419354836
 13.803879310344827
 394.8
 47.50370370370371
 94.2716049382716
 0.002512562814070352
 666.6666666666666
 410.5483870967742
 58.16201117318436
 539.4545454545454
 813.7102272727274
 549.1571753986333
 841.6168674698796
 314.4155844155844
 144.4794520547945
 36.76470588235294
 850.1002949852508
 226.0460704607046
 556.25
 286.4640883977901
 719.2
 881.7095709570957
 14.352517985611511
 997.4811083123425
 620.3783783783783
 280.1732673267327
 260.56756756756755
 0.17218543046357615
 631.3944353518822
 164.56190476190477
 228.39506172839506
 223.3919156414763
 436.6666666666667
 117.39393939393939
 424.4030552291422
 67.4004914004914
 70.48756218905473
 51.90184049079755
 437.41596638655466
 21.16923076923077
 611.4093023255814
 365.9533073929961
 0.5185185185185185
 246.75
 11.521739130434783
 163.72881355932205
 0.001402524544179523
 800.0
 370.68932038834953
 43.37916666666667
 335.19066937119675
 741.596837944664
 498.099173553719
 851.7665615141955
 493.30721003134795
 135.8253968253968
 23.214285714285715
 895.9088082901554
 107.67021276595744
 563.5883905013192
 332.37179487179486
 831.9104477611941
 886.2721617418351
 20.567010309278352
 595.6920415224914
 340.933734939759
 202.56861457649376
 0.3365695792880259
