// take care of the base case
           for i in range 1 to k:
               for j in range 0 to 2^b:
                   dp[i][j] = 0
                   for m in range 0 to 2^b:
                       // first i piles have nim-sum j
                       // ... if first i-1 piles have nim-sum m in the last
                       // ... pile we keep (m xor j) stones
                       dp[i][j] = dp[i][j] + dp[i-1][m]