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from itertools import product
 
# 定义目标数字（可根据需要修改）
TARGET = 292199
 
def find_solutions():
    a_values =  [35, 40.5, 58, 67, 73, 90.5]
    solutions_by_pair = {}
 
    total_iterations = len(a_values) ** 2 * 10000
    print(f"总计算次数: {total_iterations:,}")
 
    count = 0
    for a, b in product(a_values, repeat=2):
        min_x = 1
        max_x = int((TARGET - 1) // a)
 
        if max_x < min_x:
            continue
 
        all_solutions = []  # 存储所有解
        for x in range(min_x, max_x + 1):
            numerator = TARGET - a * x
            if numerator <= 0:
                continue
 
            y = numerator / b
            if y.is_integer() and 1 <= y <= 10000:
                all_solutions.append((x, int(y)))
 
            count += 1
            if count % 1000000 == 0:
                progress = count / total_iterations * 100
                print(f"进度: {progress:.2f}%")
 
        if all_solutions:
            # 按平衡度排序，取前2个平衡解
            balanced_solutions = sorted(all_solutions, key=lambda p: abs(p[0] - p[1]))[:2]
 
            # 从原始解中排除已在平衡解中的项，取前3个
            remaining_solutions = [s for s in all_solutions if s not in balanced_solutions][:3]
 
            # 合并：先2个平衡解，再3个原始解
            combined = balanced_solutions + remaining_solutions
 
            solutions_by_pair[(a, b)] = combined
 
    return solutions_by_pair
 
def display_solutions(solutions_by_pair):
    total_pairs = len(solutions_by_pair)
    print(f"共找到 {total_pairs} 组有效(a, b)组合，目标值为 {TARGET}")
 
    if total_pairs == 0:
        return
 
    sorted_pairs = sorted(solutions_by_pair.keys(), key=lambda x: (x[0], x[1]))
 
    for i, (a, b) in enumerate(sorted_pairs, 1):
        solutions = solutions_by_pair[(a, b)]
        print(f"\n{i}. 组合 a={a}, b={b}: {len(solutions)} 个解")
 
        for j, (x, y) in enumerate(solutions, 1):
            diff = abs(x - y)
            ax = a * x
            by = b * y
            tag = "[平衡解]" if j <= 2 else "[原始解]"
            print(f"   {j}. x={x}, y={y}  (差值: {diff}, a*x={ax}, b*y={by}, a*x + b*y = {ax + by:.1f}) {tag}")
 
if __name__ == "__main__":
    import time
    start_time = time.time()
 
    solutions_by_pair = find_solutions()
    display_solutions(solutions_by_pair)
 
    print(f"计算耗时: {time.time() - start_time:.2f}秒")

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Success #stdin #stdout 0.12s 9520KB

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Standard input is empty

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总计算次数: 360,000
共找到 30 组有效(a, b)组合，目标值为 292199

1. 组合 a=35, b=40.5: 5 个解
   1. x=3838, y=3898  (差值: 60, a*x=134330, b*y=157869.0, a*x + b*y = 292199.0) [平衡解]
   2. x=3919, y=3828  (差值: 91, a*x=137165, b*y=155034.0, a*x + b*y = 292199.0) [平衡解]
   3. x=31, y=7188  (差值: 7157, a*x=1085, b*y=291114.0, a*x + b*y = 292199.0) [原始解]
   4. x=112, y=7118  (差值: 7006, a*x=3920, b*y=288279.0, a*x + b*y = 292199.0) [原始解]
   5. x=193, y=7048  (差值: 6855, a*x=6755, b*y=285444.0, a*x + b*y = 292199.0) [原始解]

2. 组合 a=35, b=58: 5 个解
   1. x=3165, y=3128  (差值: 37, a*x=110775, b*y=181424, a*x + b*y = 292199.0) [平衡解]
   2. x=3107, y=3163  (差值: 56, a*x=108745, b*y=183454, a*x + b*y = 292199.0) [平衡解]
   3. x=33, y=5018  (差值: 4985, a*x=1155, b*y=291044, a*x + b*y = 292199.0) [原始解]
   4. x=91, y=4983  (差值: 4892, a*x=3185, b*y=289014, a*x + b*y = 292199.0) [原始解]
   5. x=149, y=4948  (差值: 4799, a*x=5215, b*y=286984, a*x + b*y = 292199.0) [原始解]

3. 组合 a=35, b=67: 5 个解
   1. x=2889, y=2852  (差值: 37, a*x=101115, b*y=191084, a*x + b*y = 292199.0) [平衡解]
   2. x=2822, y=2887  (差值: 65, a*x=98770, b*y=193429, a*x + b*y = 292199.0) [平衡解]
   3. x=8, y=4357  (差值: 4349, a*x=280, b*y=291919, a*x + b*y = 292199.0) [原始解]
   4. x=75, y=4322  (差值: 4247, a*x=2625, b*y=289574, a*x + b*y = 292199.0) [原始解]
   5. x=142, y=4287  (差值: 4145, a*x=4970, b*y=287229, a*x + b*y = 292199.0) [原始解]

4. 组合 a=35, b=73: 5 个解
   1. x=2690, y=2713  (差值: 23, a*x=94150, b*y=198049, a*x + b*y = 292199.0) [平衡解]
   2. x=2763, y=2678  (差值: 85, a*x=96705, b*y=195494, a*x + b*y = 292199.0) [平衡解]
   3. x=62, y=3973  (差值: 3911, a*x=2170, b*y=290029, a*x + b*y = 292199.0) [原始解]
   4. x=135, y=3938  (差值: 3803, a*x=4725, b*y=287474, a*x + b*y = 292199.0) [原始解]
   5. x=208, y=3903  (差值: 3695, a*x=7280, b*y=284919, a*x + b*y = 292199.0) [原始解]

5. 组合 a=35, b=90.5: 5 个解
   1. x=2329, y=2328  (差值: 1, a*x=81515, b*y=210684.0, a*x + b*y = 292199.0) [平衡解]
   2. x=2148, y=2398  (差值: 250, a*x=75180, b*y=217019.0, a*x + b*y = 292199.0) [平衡解]
   3. x=157, y=3168  (差值: 3011, a*x=5495, b*y=286704.0, a*x + b*y = 292199.0) [原始解]
   4. x=338, y=3098  (差值: 2760, a*x=11830, b*y=280369.0, a*x + b*y = 292199.0) [原始解]
   5. x=519, y=3028  (差值: 2509, a*x=18165, b*y=274034.0, a*x + b*y = 292199.0) [原始解]

6. 组合 a=40.5, b=35: 5 个解
   1. x=3898, y=3838  (差值: 60, a*x=157869.0, b*y=134330, a*x + b*y = 292199.0) [平衡解]
   2. x=3828, y=3919  (差值: 91, a*x=155034.0, b*y=137165, a*x + b*y = 292199.0) [平衡解]
   3. x=48, y=8293  (差值: 8245, a*x=1944.0, b*y=290255, a*x + b*y = 292199.0) [原始解]
   4. x=118, y=8212  (差值: 8094, a*x=4779.0, b*y=287420, a*x + b*y = 292199.0) [原始解]
   5. x=188, y=8131  (差值: 7943, a*x=7614.0, b*y=284585, a*x + b*y = 292199.0) [原始解]

7. 组合 a=40.5, b=58: 5 个解
   1. x=2950, y=2978  (差值: 28, a*x=119475.0, b*y=172724, a*x + b*y = 292199.0) [平衡解]
   2. x=3066, y=2897  (差值: 169, a*x=124173.0, b*y=168026, a*x + b*y = 292199.0) [平衡解]
   3. x=50, y=5003  (差值: 4953, a*x=2025.0, b*y=290174, a*x + b*y = 292199.0) [原始解]
   4. x=166, y=4922  (差值: 4756, a*x=6723.0, b*y=285476, a*x + b*y = 292199.0) [原始解]
   5. x=282, y=4841  (差值: 4559, a*x=11421.0, b*y=280778, a*x + b*y = 292199.0) [原始解]

8. 组合 a=40.5, b=67: 5 个解
   1. x=2720, y=2717  (差值: 3, a*x=110160.0, b*y=182039, a*x + b*y = 292199.0) [平衡解]
   2. x=2586, y=2798  (差值: 212, a*x=104733.0, b*y=187466, a*x + b*y = 292199.0) [平衡解]
   3. x=40, y=4337  (差值: 4297, a*x=1620.0, b*y=290579, a*x + b*y = 292199.0) [原始解]
   4. x=174, y=4256  (差值: 4082, a*x=7047.0, b*y=285152, a*x + b*y = 292199.0) [原始解]
   5. x=308, y=4175  (差值: 3867, a*x=12474.0, b*y=279725, a*x + b*y = 292199.0) [原始解]

9. 组合 a=40.5, b=73: 5 个解
   1. x=2550, y=2588  (差值: 38, a*x=103275.0, b*y=188924, a*x + b*y = 292199.0) [平衡解]
   2. x=2696, y=2507  (差值: 189, a*x=109188.0, b*y=183011, a*x + b*y = 292199.0) [平衡解]
   3. x=68, y=3965  (差值: 3897, a*x=2754.0, b*y=289445, a*x + b*y = 292199.0) [原始解]
   4. x=214, y=3884  (差值: 3670, a*x=8667.0, b*y=283532, a*x + b*y = 292199.0) [原始解]
   5. x=360, y=3803  (差值: 3443, a*x=14580.0, b*y=277619, a*x + b*y = 292199.0) [原始解]

10. 组合 a=40.5, b=90.5: 5 个解
   1. x=2225, y=2233  (差值: 8, a*x=90112.5, b*y=202086.5, a*x + b*y = 292199.0) [平衡解]
   2. x=2406, y=2152  (差值: 254, a*x=97443.0, b*y=194756.0, a*x + b*y = 292199.0) [平衡解]
   3. x=53, y=3205  (差值: 3152, a*x=2146.5, b*y=290052.5, a*x + b*y = 292199.0) [原始解]
   4. x=234, y=3124  (差值: 2890, a*x=9477.0, b*y=282722.0, a*x + b*y = 292199.0) [原始解]
   5. x=415, y=3043  (差值: 2628, a*x=16807.5, b*y=275391.5, a*x + b*y = 292199.0) [原始解]

11. 组合 a=58, b=35: 5 个解
   1. x=3128, y=3165  (差值: 37, a*x=181424, b*y=110775, a*x + b*y = 292199.0) [平衡解]
   2. x=3163, y=3107  (差值: 56, a*x=183454, b*y=108745, a*x + b*y = 292199.0) [平衡解]
   3. x=13, y=8327  (差值: 8314, a*x=754, b*y=291445, a*x + b*y = 292199.0) [原始解]
   4. x=48, y=8269  (差值: 8221, a*x=2784, b*y=289415, a*x + b*y = 292199.0) [原始解]
   5. x=83, y=8211  (差值: 8128, a*x=4814, b*y=287385, a*x + b*y = 292199.0) [原始解]

12. 组合 a=58, b=40.5: 5 个解
   1. x=2978, y=2950  (差值: 28, a*x=172724, b*y=119475.0, a*x + b*y = 292199.0) [平衡解]
   2. x=2897, y=3066  (差值: 169, a*x=168026, b*y=124173.0, a*x + b*y = 292199.0) [平衡解]
   3. x=62, y=7126  (差值: 7064, a*x=3596, b*y=288603.0, a*x + b*y = 292199.0) [原始解]
   4. x=143, y=7010  (差值: 6867, a*x=8294, b*y=283905.0, a*x + b*y = 292199.0) [原始解]
   5. x=224, y=6894  (差值: 6670, a*x=12992, b*y=279207.0, a*x + b*y = 292199.0) [原始解]

13. 组合 a=58, b=67: 5 个解
   1. x=2366, y=2313  (差值: 53, a*x=137228, b*y=154971, a*x + b*y = 292199.0) [平衡解]
   2. x=2299, y=2371  (差值: 72, a*x=133342, b*y=158857, a*x + b*y = 292199.0) [平衡解]
   3. x=21, y=4343  (差值: 4322, a*x=1218, b*y=290981, a*x + b*y = 292199.0) [原始解]
   4. x=88, y=4285  (差值: 4197, a*x=5104, b*y=287095, a*x + b*y = 292199.0) [原始解]
   5. x=155, y=4227  (差值: 4072, a*x=8990, b*y=283209, a*x + b*y = 292199.0) [原始解]

14. 组合 a=58, b=73: 5 个解
   1. x=2240, y=2223  (差值: 17, a*x=129920, b*y=162279, a*x + b*y = 292199.0) [平衡解]
   2. x=2167, y=2281  (差值: 114, a*x=125686, b*y=166513, a*x + b*y = 292199.0) [平衡解]
   3. x=50, y=3963  (差值: 3913, a*x=2900, b*y=289299, a*x + b*y = 292199.0) [原始解]
   4. x=123, y=3905  (差值: 3782, a*x=7134, b*y=285065, a*x + b*y = 292199.0) [原始解]
   5. x=196, y=3847  (差值: 3651, a*x=11368, b*y=280831, a*x + b*y = 292199.0) [原始解]

15. 组合 a=58, b=90.5: 5 个解
   1. x=1989, y=1954  (差值: 35, a*x=115362, b*y=176837.0, a*x + b*y = 292199.0) [平衡解]
   2. x=1808, y=2070  (差值: 262, a*x=104864, b*y=187335.0, a*x + b*y = 292199.0) [平衡解]
   3. x=179, y=3114  (差值: 2935, a*x=10382, b*y=281817.0, a*x + b*y = 292199.0) [原始解]
   4. x=360, y=2998  (差值: 2638, a*x=20880, b*y=271319.0, a*x + b*y = 292199.0) [原始解]
   5. x=541, y=2882  (差值: 2341, a*x=31378, b*y=260821.0, a*x + b*y = 292199.0) [原始解]

16. 组合 a=67, b=35: 5 个解
   1. x=2852, y=2889  (差值: 37, a*x=191084, b*y=101115, a*x + b*y = 292199.0) [平衡解]
   2. x=2887, y=2822  (差值: 65, a*x=193429, b*y=98770, a*x + b*y = 292199.0) [平衡解]
   3. x=17, y=8316  (差值: 8299, a*x=1139, b*y=291060, a*x + b*y = 292199.0) [原始解]
   4. x=52, y=8249  (差值: 8197, a*x=3484, b*y=288715, a*x + b*y = 292199.0) [原始解]
   5. x=87, y=8182  (差值: 8095, a*x=5829, b*y=286370, a*x + b*y = 292199.0) [原始解]

17. 组合 a=67, b=40.5: 5 个解
   1. x=2717, y=2720  (差值: 3, a*x=182039, b*y=110160.0, a*x + b*y = 292199.0) [平衡解]
   2. x=2798, y=2586  (差值: 212, a*x=187466, b*y=104733.0, a*x + b*y = 292199.0) [平衡解]
   3. x=44, y=7142  (差值: 7098, a*x=2948, b*y=289251.0, a*x + b*y = 292199.0) [原始解]
   4. x=125, y=7008  (差值: 6883, a*x=8375, b*y=283824.0, a*x + b*y = 292199.0) [原始解]
   5. x=206, y=6874  (差值: 6668, a*x=13802, b*y=278397.0, a*x + b*y = 292199.0) [原始解]

18. 组合 a=67, b=58: 5 个解
   1. x=2313, y=2366  (差值: 53, a*x=154971, b*y=137228, a*x + b*y = 292199.0) [平衡解]
   2. x=2371, y=2299  (差值: 72, a*x=158857, b*y=133342, a*x + b*y = 292199.0) [平衡解]
   3. x=51, y=4979  (差值: 4928, a*x=3417, b*y=288782, a*x + b*y = 292199.0) [原始解]
   4. x=109, y=4912  (差值: 4803, a*x=7303, b*y=284896, a*x + b*y = 292199.0) [原始解]
   5. x=167, y=4845  (差值: 4678, a*x=11189, b*y=281010, a*x + b*y = 292199.0) [原始解]

19. 组合 a=67, b=73: 5 个解
   1. x=2096, y=2079  (差值: 17, a*x=140432, b*y=151767, a*x + b*y = 292199.0) [平衡解]
   2. x=2023, y=2146  (差值: 123, a*x=135541, b*y=156658, a*x + b*y = 292199.0) [平衡解]
   3. x=52, y=3955  (差值: 3903, a*x=3484, b*y=288715, a*x + b*y = 292199.0) [原始解]
   4. x=125, y=3888  (差值: 3763, a*x=8375, b*y=283824, a*x + b*y = 292199.0) [原始解]
   5. x=198, y=3821  (差值: 3623, a*x=13266, b*y=278933, a*x + b*y = 292199.0) [原始解]

20. 组合 a=67, b=90.5: 5 个解
   1. x=1865, y=1848  (差值: 17, a*x=124955, b*y=167244.0, a*x + b*y = 292199.0) [平衡解]
   2. x=1684, y=1982  (差值: 298, a*x=112828, b*y=179371.0, a*x + b*y = 292199.0) [平衡解]
   3. x=55, y=3188  (差值: 3133, a*x=3685, b*y=288514.0, a*x + b*y = 292199.0) [原始解]
   4. x=236, y=3054  (差值: 2818, a*x=15812, b*y=276387.0, a*x + b*y = 292199.0) [原始解]
   5. x=417, y=2920  (差值: 2503, a*x=27939, b*y=264260.0, a*x + b*y = 292199.0) [原始解]

21. 组合 a=73, b=35: 5 个解
   1. x=2713, y=2690  (差值: 23, a*x=198049, b*y=94150, a*x + b*y = 292199.0) [平衡解]
   2. x=2678, y=2763  (差值: 85, a*x=195494, b*y=96705, a*x + b*y = 292199.0) [平衡解]
   3. x=18, y=8311  (差值: 8293, a*x=1314, b*y=290885, a*x + b*y = 292199.0) [原始解]
   4. x=53, y=8238  (差值: 8185, a*x=3869, b*y=288330, a*x + b*y = 292199.0) [原始解]
   5. x=88, y=8165  (差值: 8077, a*x=6424, b*y=285775, a*x + b*y = 292199.0) [原始解]

22. 组合 a=73, b=40.5: 5 个解
   1. x=2588, y=2550  (差值: 38, a*x=188924, b*y=103275.0, a*x + b*y = 292199.0) [平衡解]
   2. x=2507, y=2696  (差值: 189, a*x=183011, b*y=109188.0, a*x + b*y = 292199.0) [平衡解]
   3. x=77, y=7076  (差值: 6999, a*x=5621, b*y=286578.0, a*x + b*y = 292199.0) [原始解]
   4. x=158, y=6930  (差值: 6772, a*x=11534, b*y=280665.0, a*x + b*y = 292199.0) [原始解]
   5. x=239, y=6784  (差值: 6545, a*x=17447, b*y=274752.0, a*x + b*y = 292199.0) [原始解]

23. 组合 a=73, b=58: 5 个解
   1. x=2223, y=2240  (差值: 17, a*x=162279, b*y=129920, a*x + b*y = 292199.0) [平衡解]
   2. x=2281, y=2167  (差值: 114, a*x=166513, b*y=125686, a*x + b*y = 292199.0) [平衡解]
   3. x=19, y=5014  (差值: 4995, a*x=1387, b*y=290812, a*x + b*y = 292199.0) [原始解]
   4. x=77, y=4941  (差值: 4864, a*x=5621, b*y=286578, a*x + b*y = 292199.0) [原始解]
   5. x=135, y=4868  (差值: 4733, a*x=9855, b*y=282344, a*x + b*y = 292199.0) [原始解]

24. 组合 a=73, b=67: 5 个解
   1. x=2079, y=2096  (差值: 17, a*x=151767, b*y=140432, a*x + b*y = 292199.0) [平衡解]
   2. x=2146, y=2023  (差值: 123, a*x=156658, b*y=135541, a*x + b*y = 292199.0) [平衡解]
   3. x=2, y=4359  (差值: 4357, a*x=146, b*y=292053, a*x + b*y = 292199.0) [原始解]
   4. x=69, y=4286  (差值: 4217, a*x=5037, b*y=287162, a*x + b*y = 292199.0) [原始解]
   5. x=136, y=4213  (差值: 4077, a*x=9928, b*y=282271, a*x + b*y = 292199.0) [原始解]

25. 组合 a=73, b=90.5: 5 个解
   1. x=1858, y=1730  (差值: 128, a*x=135634, b*y=156565.0, a*x + b*y = 292199.0) [平衡解]
   2. x=1677, y=1876  (差值: 199, a*x=122421, b*y=169778.0, a*x + b*y = 292199.0) [平衡解]
   3. x=48, y=3190  (差值: 3142, a*x=3504, b*y=288695.0, a*x + b*y = 292199.0) [原始解]
   4. x=229, y=3044  (差值: 2815, a*x=16717, b*y=275482.0, a*x + b*y = 292199.0) [原始解]
   5. x=410, y=2898  (差值: 2488, a*x=29930, b*y=262269.0, a*x + b*y = 292199.0) [原始解]

26. 组合 a=90.5, b=35: 5 个解
   1. x=2328, y=2329  (差值: 1, a*x=210684.0, b*y=81515, a*x + b*y = 292199.0) [平衡解]
   2. x=2398, y=2148  (差值: 250, a*x=217019.0, b*y=75180, a*x + b*y = 292199.0) [平衡解]
   3. x=18, y=8302  (差值: 8284, a*x=1629.0, b*y=290570, a*x + b*y = 292199.0) [原始解]
   4. x=88, y=8121  (差值: 8033, a*x=7964.0, b*y=284235, a*x + b*y = 292199.0) [原始解]
   5. x=158, y=7940  (差值: 7782, a*x=14299.0, b*y=277900, a*x + b*y = 292199.0) [原始解]

27. 组合 a=90.5, b=40.5: 5 个解
   1. x=2233, y=2225  (差值: 8, a*x=202086.5, b*y=90112.5, a*x + b*y = 292199.0) [平衡解]
   2. x=2152, y=2406  (差值: 254, a*x=194756.0, b*y=97443.0, a*x + b*y = 292199.0) [平衡解]
   3. x=46, y=7112  (差值: 7066, a*x=4163.0, b*y=288036.0, a*x + b*y = 292199.0) [原始解]
   4. x=127, y=6931  (差值: 6804, a*x=11493.5, b*y=280705.5, a*x + b*y = 292199.0) [原始解]
   5. x=208, y=6750  (差值: 6542, a*x=18824.0, b*y=273375.0, a*x + b*y = 292199.0) [原始解]

28. 组合 a=90.5, b=58: 5 个解
   1. x=1954, y=1989  (差值: 35, a*x=176837.0, b*y=115362, a*x + b*y = 292199.0) [平衡解]
   2. x=2070, y=1808  (差值: 262, a*x=187335.0, b*y=104864, a*x + b*y = 292199.0) [平衡解]
   3. x=98, y=4885  (差值: 4787, a*x=8869.0, b*y=283330, a*x + b*y = 292199.0) [原始解]
   4. x=214, y=4704  (差值: 4490, a*x=19367.0, b*y=272832, a*x + b*y = 292199.0) [原始解]
   5. x=330, y=4523  (差值: 4193, a*x=29865.0, b*y=262334, a*x + b*y = 292199.0) [原始解]

29. 组合 a=90.5, b=67: 5 个解
   1. x=1848, y=1865  (差值: 17, a*x=167244.0, b*y=124955, a*x + b*y = 292199.0) [平衡解]
   2. x=1982, y=1684  (差值: 298, a*x=179371.0, b*y=112828, a*x + b*y = 292199.0) [平衡解]
   3. x=106, y=4218  (差值: 4112, a*x=9593.0, b*y=282606, a*x + b*y = 292199.0) [原始解]
   4. x=240, y=4037  (差值: 3797, a*x=21720.0, b*y=270479, a*x + b*y = 292199.0) [原始解]
   5. x=374, y=3856  (差值: 3482, a*x=33847.0, b*y=258352, a*x + b*y = 292199.0) [原始解]

30. 组合 a=90.5, b=73: 5 个解
   1. x=1730, y=1858  (差值: 128, a*x=156565.0, b*y=135634, a*x + b*y = 292199.0) [平衡解]
   2. x=1876, y=1677  (差值: 199, a*x=169778.0, b*y=122421, a*x + b*y = 292199.0) [平衡解]
   3. x=124, y=3849  (差值: 3725, a*x=11222.0, b*y=280977, a*x + b*y = 292199.0) [原始解]
   4. x=270, y=3668  (差值: 3398, a*x=24435.0, b*y=267764, a*x + b*y = 292199.0) [原始解]
   5. x=416, y=3487  (差值: 3071, a*x=37648.0, b*y=254551, a*x + b*y = 292199.0) [原始解]
计算耗时: 0.09秒

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Python 3 nbc (python 3.7.3)

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