Strange Nim

grundy_A150_K10.txt

  X  g
-------
  0  0
  1  0
  2  0
  3  0
  4  0
  5  0
  6  0
  7  0
  8  0
  9  0
 10  1
 11  0
 12  1
 13  0
 14  1
 15  0
 16  1
 17  0
 18  1
 19  0
 20  2
 21  1
 22  0
 23  2
 24  1
 25  0
 26  2
 27  1
 28  0
 29  2
 30  3
 31  1
 32  0
 33  2
 34  3
 35  1
 36  0
 37  2
 38  3
 39  1
 40  4
 41  0
 42  2
 43  3
 44  1
 45  4
 46  0
 47  2
 48  3
 49  1
 50  5
 51  4
 52  0
 53  2
 54  3
 55  1
 56  5
 57  4
 58  0
 59  2
 60  6
 61  3
 62  1
 63  5
 64  4
 65  0
 66  2
 67  6
 68  3
 69  1
 70  7
 71  5
 72  4
 73  0
 74  2
 75  6
 76  3
 77  1
 78  7
 79  5
 80  8
 81  4
 82  0
 83  2
 84  6
 85  3
 86  1
 87  7
 88  5
 89  8
 90  9
 91  4
 92  0
 93  2
 94  6
 95  3
 96  1
 97  7
 98  5
 99  8
100 10
101  9
102  4
103  0
104  2
105  6
106  3
107  1
108  7
109  5
110 11
111  8
112 10
113  9
114  4
115  0
116  2
117  6
118  3
119  1
120 12
121  7
122  5
123 11
124  8
125 10
126  9
127  4
128  0
129  2
130 13
131  6
132  3
133  1
134 12
135  7
136  5
137 11
138  8
139 10
140 14
141  9
142  4
143  0
144  2
145 13
146  6
147  3
148  1
149 12
150 15

test.rb

A, K = gets.split.map(&:to_i)
grundy = [0]
(1..A).each do |i|
    exist = Array.new(i+1)
    (i-1).downto(i-i/K) do |j|
        exist[grundy[j]] = true
    end
    (i+1).times do |j|
        unless exist[j]
            grundy[i] = j
            break
        end
    end
end
(A+1).times do |i|
    puts sprintf("%3d %2d", i, grundy[i])
end