Project Euler #172: Investigating numbers with few repeated digits

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    Cannot make my program work correctly and will move to another project. I think I made some mistakes on some assumption but cannot figure it out. But I did learn a lot from this project. Learn the Fermat's theorem and know how to calculate large modulus on exponential, factorials, and combinations. Lots of trick on how to squeeze the performance.

    I used brutal force to get the following results, hope they are helpful for you.

    k = 1
    m = 0
    0
    
    k = 1
    m = 1
    9
    
    k = 2
    m = 0
    0
    
    k = 2
    m = 1
    81
    
    k = 2
    m = 2
    90
    
    k = 3
    m = 0
    0
    
    k = 3
    m = 1
    648
    
    k = 3
    m = 2
    891
    
    k = 3
    m = 3
    900
    
    k = 4
    m = 0
    0
    
    k = 4
    m = 1
    4536
    
    k = 4
    m = 2
    8667
    
    k = 4
    m = 3
    8991
    
    k = 4
    m = 4
    9000
    
    k = 5
    m = 0
    0
    
    k = 5
    m = 1
    27216
    
    k = 5
    m = 2
    82296
    
    k = 5
    m = 3
    89586
    
    k = 5
    m = 4
    89991
    
    k = 5
    m = 5
    90000
    
    k = 6
    m = 0
    0
    
    k = 6
    m = 1
    136080
    
    k = 6
    m = 2
    758160
    
    k = 6
    m = 3
    888570
    
    k = 6
    m = 4
    899505
    
    k = 6
    m = 5
    899991
    
    k = 6
    m = 6
    900000
    
    k = 7
    m = 0
    0
    
    k = 7
    m = 1
    544320
    
    k = 7
    m = 2
    6735960
    
    k = 7
    m = 3
    8754480
    
    k = 7
    m = 4
    8984115
    
    k = 7
    m = 5
    8999424
    
    k = 7
    m = 6
    8999991
    
    k = 7
    m = 7
    9000000