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from itertools import product
 
# 定义目标数字（可根据需要修改）
TARGET = 335900
 
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 0.07s 9692KB

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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 335900

1. 组合 a=35, b=40.5: 5 个解
   1. x=4471, y=4430  (差值: 41, a*x=156485, b*y=179415.0, a*x + b*y = 335900.0) [平衡解]
   2. x=4390, y=4500  (差值: 110, a*x=153650, b*y=182250.0, a*x + b*y = 335900.0) [平衡解]
   3. x=16, y=8280  (差值: 8264, a*x=560, b*y=335340.0, a*x + b*y = 335900.0) [原始解]
   4. x=97, y=8210  (差值: 8113, a*x=3395, b*y=332505.0, a*x + b*y = 335900.0) [原始解]
   5. x=178, y=8140  (差值: 7962, a*x=6230, b*y=329670.0, a*x + b*y = 335900.0) [原始解]

2. 组合 a=35, b=58: 5 个解
   1. x=3590, y=3625  (差值: 35, a*x=125650, b*y=210250, a*x + b*y = 335900.0) [平衡解]
   2. x=3648, y=3590  (差值: 58, a*x=127680, b*y=208220, a*x + b*y = 335900.0) [平衡解]
   3. x=52, y=5760  (差值: 5708, a*x=1820, b*y=334080, a*x + b*y = 335900.0) [原始解]
   4. x=110, y=5725  (差值: 5615, a*x=3850, b*y=332050, a*x + b*y = 335900.0) [原始解]
   5. x=168, y=5690  (差值: 5522, a*x=5880, b*y=330020, a*x + b*y = 335900.0) [原始解]

3. 组合 a=35, b=67: 5 个解
   1. x=3280, y=3300  (差值: 20, a*x=114800, b*y=221100, a*x + b*y = 335900.0) [平衡解]
   2. x=3347, y=3265  (差值: 82, a*x=117145, b*y=218755, a*x + b*y = 335900.0) [平衡解]
   3. x=64, y=4980  (差值: 4916, a*x=2240, b*y=333660, a*x + b*y = 335900.0) [原始解]
   4. x=131, y=4945  (差值: 4814, a*x=4585, b*y=331315, a*x + b*y = 335900.0) [原始解]
   5. x=198, y=4910  (差值: 4712, a*x=6930, b*y=328970, a*x + b*y = 335900.0) [原始解]

4. 组合 a=35, b=73: 5 个解
   1. x=3121, y=3105  (差值: 16, a*x=109235, b*y=226665, a*x + b*y = 335900.0) [平衡解]
   2. x=3048, y=3140  (差值: 92, a*x=106680, b*y=229220, a*x + b*y = 335900.0) [平衡解]
   3. x=55, y=4575  (差值: 4520, a*x=1925, b*y=333975, a*x + b*y = 335900.0) [原始解]
   4. x=128, y=4540  (差值: 4412, a*x=4480, b*y=331420, a*x + b*y = 335900.0) [原始解]
   5. x=201, y=4505  (差值: 4304, a*x=7035, b*y=328865, a*x + b*y = 335900.0) [原始解]

5. 组合 a=35, b=90.5: 5 个解
   1. x=2745, y=2650  (差值: 95, a*x=96075, b*y=239825.0, a*x + b*y = 335900.0) [平衡解]
   2. x=2564, y=2720  (差值: 156, a*x=89740, b*y=246160.0, a*x + b*y = 335900.0) [平衡解]
   3. x=30, y=3700  (差值: 3670, a*x=1050, b*y=334850.0, a*x + b*y = 335900.0) [原始解]
   4. x=211, y=3630  (差值: 3419, a*x=7385, b*y=328515.0, a*x + b*y = 335900.0) [原始解]
   5. x=392, y=3560  (差值: 3168, a*x=13720, b*y=322180.0, a*x + b*y = 335900.0) [原始解]

6. 组合 a=40.5, b=35: 5 个解
   1. x=4430, y=4471  (差值: 41, a*x=179415.0, b*y=156485, a*x + b*y = 335900.0) [平衡解]
   2. x=4500, y=4390  (差值: 110, a*x=182250.0, b*y=153650, a*x + b*y = 335900.0) [平衡解]
   3. x=20, y=9574  (差值: 9554, a*x=810.0, b*y=335090, a*x + b*y = 335900.0) [原始解]
   4. x=90, y=9493  (差值: 9403, a*x=3645.0, b*y=332255, a*x + b*y = 335900.0) [原始解]
   5. x=160, y=9412  (差值: 9252, a*x=6480.0, b*y=329420, a*x + b*y = 335900.0) [原始解]

7. 组合 a=40.5, b=58: 5 个解
   1. x=3376, y=3434  (差值: 58, a*x=136728.0, b*y=199172, a*x + b*y = 335900.0) [平衡解]
   2. x=3492, y=3353  (差值: 139, a*x=141426.0, b*y=194474, a*x + b*y = 335900.0) [平衡解]
   3. x=12, y=5783  (差值: 5771, a*x=486.0, b*y=335414, a*x + b*y = 335900.0) [原始解]
   4. x=128, y=5702  (差值: 5574, a*x=5184.0, b*y=330716, a*x + b*y = 335900.0) [原始解]
   5. x=244, y=5621  (差值: 5377, a*x=9882.0, b*y=326018, a*x + b*y = 335900.0) [原始解]

8. 组合 a=40.5, b=67: 5 个解
   1. x=3134, y=3119  (差值: 15, a*x=126927.0, b*y=208973, a*x + b*y = 335900.0) [平衡解]
   2. x=3000, y=3200  (差值: 200, a*x=121500.0, b*y=214400, a*x + b*y = 335900.0) [平衡解]
   3. x=52, y=4982  (差值: 4930, a*x=2106.0, b*y=333794, a*x + b*y = 335900.0) [原始解]
   4. x=186, y=4901  (差值: 4715, a*x=7533.0, b*y=328367, a*x + b*y = 335900.0) [原始解]
   5. x=320, y=4820  (差值: 4500, a*x=12960.0, b*y=322940, a*x + b*y = 335900.0) [原始解]

9. 组合 a=40.5, b=73: 5 个解
   1. x=3018, y=2927  (差值: 91, a*x=122229.0, b*y=213671, a*x + b*y = 335900.0) [平衡解]
   2. x=2872, y=3008  (差值: 136, a*x=116316.0, b*y=219584, a*x + b*y = 335900.0) [平衡解]
   3. x=98, y=4547  (差值: 4449, a*x=3969.0, b*y=331931, a*x + b*y = 335900.0) [原始解]
   4. x=244, y=4466  (差值: 4222, a*x=9882.0, b*y=326018, a*x + b*y = 335900.0) [原始解]
   5. x=390, y=4385  (差值: 3995, a*x=15795.0, b*y=320105, a*x + b*y = 335900.0) [原始解]

10. 组合 a=40.5, b=90.5: 5 个解
   1. x=2513, y=2587  (差值: 74, a*x=101776.5, b*y=234123.5, a*x + b*y = 335900.0) [平衡解]
   2. x=2694, y=2506  (差值: 188, a*x=109107.0, b*y=226793.0, a*x + b*y = 335900.0) [平衡解]
   3. x=160, y=3640  (差值: 3480, a*x=6480.0, b*y=329420.0, a*x + b*y = 335900.0) [原始解]
   4. x=341, y=3559  (差值: 3218, a*x=13810.5, b*y=322089.5, a*x + b*y = 335900.0) [原始解]
   5. x=522, y=3478  (差值: 2956, a*x=21141.0, b*y=314759.0, a*x + b*y = 335900.0) [原始解]

11. 组合 a=58, b=35: 5 个解
   1. x=3625, y=3590  (差值: 35, a*x=210250, b*y=125650, a*x + b*y = 335900.0) [平衡解]
   2. x=3590, y=3648  (差值: 58, a*x=208220, b*y=127680, a*x + b*y = 335900.0) [平衡解]
   3. x=20, y=9564  (差值: 9544, a*x=1160, b*y=334740, a*x + b*y = 335900.0) [原始解]
   4. x=55, y=9506  (差值: 9451, a*x=3190, b*y=332710, a*x + b*y = 335900.0) [原始解]
   5. x=90, y=9448  (差值: 9358, a*x=5220, b*y=330680, a*x + b*y = 335900.0) [原始解]

12. 组合 a=58, b=40.5: 5 个解
   1. x=3434, y=3376  (差值: 58, a*x=199172, b*y=136728.0, a*x + b*y = 335900.0) [平衡解]
   2. x=3353, y=3492  (差值: 139, a*x=194474, b*y=141426.0, a*x + b*y = 335900.0) [平衡解]
   3. x=32, y=8248  (差值: 8216, a*x=1856, b*y=334044.0, a*x + b*y = 335900.0) [原始解]
   4. x=113, y=8132  (差值: 8019, a*x=6554, b*y=329346.0, a*x + b*y = 335900.0) [原始解]
   5. x=194, y=8016  (差值: 7822, a*x=11252, b*y=324648.0, a*x + b*y = 335900.0) [原始解]

13. 组合 a=58, b=67: 5 个解
   1. x=2714, y=2664  (差值: 50, a*x=157412, b*y=178488, a*x + b*y = 335900.0) [平衡解]
   2. x=2647, y=2722  (差值: 75, a*x=153526, b*y=182374, a*x + b*y = 335900.0) [平衡解]
   3. x=34, y=4984  (差值: 4950, a*x=1972, b*y=333928, a*x + b*y = 335900.0) [原始解]
   4. x=101, y=4926  (差值: 4825, a*x=5858, b*y=330042, a*x + b*y = 335900.0) [原始解]
   5. x=168, y=4868  (差值: 4700, a*x=9744, b*y=326156, a*x + b*y = 335900.0) [原始解]

14. 组合 a=58, b=73: 5 个解
   1. x=2597, y=2538  (差值: 59, a*x=150626, b*y=185274, a*x + b*y = 335900.0) [平衡解]
   2. x=2524, y=2596  (差值: 72, a*x=146392, b*y=189508, a*x + b*y = 335900.0) [平衡解]
   3. x=42, y=4568  (差值: 4526, a*x=2436, b*y=333464, a*x + b*y = 335900.0) [原始解]
   4. x=115, y=4510  (差值: 4395, a*x=6670, b*y=329230, a*x + b*y = 335900.0) [原始解]
   5. x=188, y=4452  (差值: 4264, a*x=10904, b*y=324996, a*x + b*y = 335900.0) [原始解]

15. 组合 a=58, b=90.5: 5 个解
   1. x=2265, y=2260  (差值: 5, a*x=131370, b*y=204530.0, a*x + b*y = 335900.0) [平衡解]
   2. x=2084, y=2376  (差值: 292, a*x=120872, b*y=215028.0, a*x + b*y = 335900.0) [平衡解]
   3. x=93, y=3652  (差值: 3559, a*x=5394, b*y=330506.0, a*x + b*y = 335900.0) [原始解]
   4. x=274, y=3536  (差值: 3262, a*x=15892, b*y=320008.0, a*x + b*y = 335900.0) [原始解]
   5. x=455, y=3420  (差值: 2965, a*x=26390, b*y=309510.0, a*x + b*y = 335900.0) [原始解]

16. 组合 a=67, b=35: 5 个解
   1. x=3300, y=3280  (差值: 20, a*x=221100, b*y=114800, a*x + b*y = 335900.0) [平衡解]
   2. x=3265, y=3347  (差值: 82, a*x=218755, b*y=117145, a*x + b*y = 335900.0) [平衡解]
   3. x=10, y=9578  (差值: 9568, a*x=670, b*y=335230, a*x + b*y = 335900.0) [原始解]
   4. x=45, y=9511  (差值: 9466, a*x=3015, b*y=332885, a*x + b*y = 335900.0) [原始解]
   5. x=80, y=9444  (差值: 9364, a*x=5360, b*y=330540, a*x + b*y = 335900.0) [原始解]

17. 组合 a=67, b=40.5: 5 个解
   1. x=3119, y=3134  (差值: 15, a*x=208973, b*y=126927.0, a*x + b*y = 335900.0) [平衡解]
   2. x=3200, y=3000  (差值: 200, a*x=214400, b*y=121500.0, a*x + b*y = 335900.0) [平衡解]
   3. x=41, y=8226  (差值: 8185, a*x=2747, b*y=333153.0, a*x + b*y = 335900.0) [原始解]
   4. x=122, y=8092  (差值: 7970, a*x=8174, b*y=327726.0, a*x + b*y = 335900.0) [原始解]
   5. x=203, y=7958  (差值: 7755, a*x=13601, b*y=322299.0, a*x + b*y = 335900.0) [原始解]

18. 组合 a=67, b=58: 5 个解
   1. x=2664, y=2714  (差值: 50, a*x=178488, b*y=157412, a*x + b*y = 335900.0) [平衡解]
   2. x=2722, y=2647  (差值: 75, a*x=182374, b*y=153526, a*x + b*y = 335900.0) [平衡解]
   3. x=54, y=5729  (差值: 5675, a*x=3618, b*y=332282, a*x + b*y = 335900.0) [原始解]
   4. x=112, y=5662  (差值: 5550, a*x=7504, b*y=328396, a*x + b*y = 335900.0) [原始解]
   5. x=170, y=5595  (差值: 5425, a*x=11390, b*y=324510, a*x + b*y = 335900.0) [原始解]

19. 组合 a=67, b=73: 5 个解
   1. x=2368, y=2428  (差值: 60, a*x=158656, b*y=177244, a*x + b*y = 335900.0) [平衡解]
   2. x=2441, y=2361  (差值: 80, a*x=163547, b*y=172353, a*x + b*y = 335900.0) [平衡解]
   3. x=32, y=4572  (差值: 4540, a*x=2144, b*y=333756, a*x + b*y = 335900.0) [原始解]
   4. x=105, y=4505  (差值: 4400, a*x=7035, b*y=328865, a*x + b*y = 335900.0) [原始解]
   5. x=178, y=4438  (差值: 4260, a*x=11926, b*y=323974, a*x + b*y = 335900.0) [原始解]

20. 组合 a=67, b=90.5: 5 个解
   1. x=2058, y=2188  (差值: 130, a*x=137886, b*y=198014.0, a*x + b*y = 335900.0) [平衡解]
   2. x=2239, y=2054  (差值: 185, a*x=150013, b*y=185887.0, a*x + b*y = 335900.0) [平衡解]
   3. x=67, y=3662  (差值: 3595, a*x=4489, b*y=331411.0, a*x + b*y = 335900.0) [原始解]
   4. x=248, y=3528  (差值: 3280, a*x=16616, b*y=319284.0, a*x + b*y = 335900.0) [原始解]
   5. x=429, y=3394  (差值: 2965, a*x=28743, b*y=307157.0, a*x + b*y = 335900.0) [原始解]

21. 组合 a=73, b=35: 5 个解
   1. x=3105, y=3121  (差值: 16, a*x=226665, b*y=109235, a*x + b*y = 335900.0) [平衡解]
   2. x=3140, y=3048  (差值: 92, a*x=229220, b*y=106680, a*x + b*y = 335900.0) [平衡解]
   3. x=25, y=9545  (差值: 9520, a*x=1825, b*y=334075, a*x + b*y = 335900.0) [原始解]
   4. x=60, y=9472  (差值: 9412, a*x=4380, b*y=331520, a*x + b*y = 335900.0) [原始解]
   5. x=95, y=9399  (差值: 9304, a*x=6935, b*y=328965, a*x + b*y = 335900.0) [原始解]

22. 组合 a=73, b=40.5: 5 个解
   1. x=2927, y=3018  (差值: 91, a*x=213671, b*y=122229.0, a*x + b*y = 335900.0) [平衡解]
   2. x=3008, y=2872  (差值: 136, a*x=219584, b*y=116316.0, a*x + b*y = 335900.0) [平衡解]
   3. x=11, y=8274  (差值: 8263, a*x=803, b*y=335097.0, a*x + b*y = 335900.0) [原始解]
   4. x=92, y=8128  (差值: 8036, a*x=6716, b*y=329184.0, a*x + b*y = 335900.0) [原始解]
   5. x=173, y=7982  (差值: 7809, a*x=12629, b*y=323271.0, a*x + b*y = 335900.0) [原始解]

23. 组合 a=73, b=58: 5 个解
   1. x=2538, y=2597  (差值: 59, a*x=185274, b*y=150626, a*x + b*y = 335900.0) [平衡解]
   2. x=2596, y=2524  (差值: 72, a*x=189508, b*y=146392, a*x + b*y = 335900.0) [平衡解]
   3. x=44, y=5736  (差值: 5692, a*x=3212, b*y=332688, a*x + b*y = 335900.0) [原始解]
   4. x=102, y=5663  (差值: 5561, a*x=7446, b*y=328454, a*x + b*y = 335900.0) [原始解]
   5. x=160, y=5590  (差值: 5430, a*x=11680, b*y=324220, a*x + b*y = 335900.0) [原始解]

24. 组合 a=73, b=67: 5 个解
   1. x=2428, y=2368  (差值: 60, a*x=177244, b*y=158656, a*x + b*y = 335900.0) [平衡解]
   2. x=2361, y=2441  (差值: 80, a*x=172353, b*y=163547, a*x + b*y = 335900.0) [平衡解]
   3. x=16, y=4996  (差值: 4980, a*x=1168, b*y=334732, a*x + b*y = 335900.0) [原始解]
   4. x=83, y=4923  (差值: 4840, a*x=6059, b*y=329841, a*x + b*y = 335900.0) [原始解]
   5. x=150, y=4850  (差值: 4700, a*x=10950, b*y=324950, a*x + b*y = 335900.0) [原始解]

25. 组合 a=73, b=90.5: 5 个解
   1. x=2112, y=2008  (差值: 104, a*x=154176, b*y=181724.0, a*x + b*y = 335900.0) [平衡解]
   2. x=1931, y=2154  (差值: 223, a*x=140963, b*y=194937.0, a*x + b*y = 335900.0) [平衡解]
   3. x=121, y=3614  (差值: 3493, a*x=8833, b*y=327067.0, a*x + b*y = 335900.0) [原始解]
   4. x=302, y=3468  (差值: 3166, a*x=22046, b*y=313854.0, a*x + b*y = 335900.0) [原始解]
   5. x=483, y=3322  (差值: 2839, a*x=35259, b*y=300641.0, a*x + b*y = 335900.0) [原始解]

26. 组合 a=90.5, b=35: 5 个解
   1. x=2650, y=2745  (差值: 95, a*x=239825.0, b*y=96075, a*x + b*y = 335900.0) [平衡解]
   2. x=2720, y=2564  (差值: 156, a*x=246160.0, b*y=89740, a*x + b*y = 335900.0) [平衡解]
   3. x=60, y=9442  (差值: 9382, a*x=5430.0, b*y=330470, a*x + b*y = 335900.0) [原始解]
   4. x=130, y=9261  (差值: 9131, a*x=11765.0, b*y=324135, a*x + b*y = 335900.0) [原始解]
   5. x=200, y=9080  (差值: 8880, a*x=18100.0, b*y=317800, a*x + b*y = 335900.0) [原始解]

27. 组合 a=90.5, b=40.5: 5 个解
   1. x=2587, y=2513  (差值: 74, a*x=234123.5, b*y=101776.5, a*x + b*y = 335900.0) [平衡解]
   2. x=2506, y=2694  (差值: 188, a*x=226793.0, b*y=109107.0, a*x + b*y = 335900.0) [平衡解]
   3. x=76, y=8124  (差值: 8048, a*x=6878.0, b*y=329022.0, a*x + b*y = 335900.0) [原始解]
   4. x=157, y=7943  (差值: 7786, a*x=14208.5, b*y=321691.5, a*x + b*y = 335900.0) [原始解]
   5. x=238, y=7762  (差值: 7524, a*x=21539.0, b*y=314361.0, a*x + b*y = 335900.0) [原始解]

28. 组合 a=90.5, b=58: 5 个解
   1. x=2260, y=2265  (差值: 5, a*x=204530.0, b*y=131370, a*x + b*y = 335900.0) [平衡解]
   2. x=2376, y=2084  (差值: 292, a*x=215028.0, b*y=120872, a*x + b*y = 335900.0) [平衡解]
   3. x=56, y=5704  (差值: 5648, a*x=5068.0, b*y=330832, a*x + b*y = 335900.0) [原始解]
   4. x=172, y=5523  (差值: 5351, a*x=15566.0, b*y=320334, a*x + b*y = 335900.0) [原始解]
   5. x=288, y=5342  (差值: 5054, a*x=26064.0, b*y=309836, a*x + b*y = 335900.0) [原始解]

29. 组合 a=90.5, b=67: 5 个解
   1. x=2188, y=2058  (差值: 130, a*x=198014.0, b*y=137886, a*x + b*y = 335900.0) [平衡解]
   2. x=2054, y=2239  (差值: 185, a*x=185887.0, b*y=150013, a*x + b*y = 335900.0) [平衡解]
   3. x=44, y=4954  (差值: 4910, a*x=3982.0, b*y=331918, a*x + b*y = 335900.0) [原始解]
   4. x=178, y=4773  (差值: 4595, a*x=16109.0, b*y=319791, a*x + b*y = 335900.0) [原始解]
   5. x=312, y=4592  (差值: 4280, a*x=28236.0, b*y=307664, a*x + b*y = 335900.0) [原始解]

30. 组合 a=90.5, b=73: 5 个解
   1. x=2008, y=2112  (差值: 104, a*x=181724.0, b*y=154176, a*x + b*y = 335900.0) [平衡解]
   2. x=2154, y=1931  (差值: 223, a*x=194937.0, b*y=140963, a*x + b*y = 335900.0) [平衡解]
   3. x=110, y=4465  (差值: 4355, a*x=9955.0, b*y=325945, a*x + b*y = 335900.0) [原始解]
   4. x=256, y=4284  (差值: 4028, a*x=23168.0, b*y=312732, a*x + b*y = 335900.0) [原始解]
   5. x=402, y=4103  (差值: 3701, a*x=36381.0, b*y=299519, a*x + b*y = 335900.0) [原始解]
计算耗时: 0.05秒

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