HDU 3032 Nim or not Nim? (SG function in game)

Q: the transformation of the classic Nim game gives you n heap stones pi, each Heap has pi stones,

Alice and Bob take turns to take stones. Each time they take any stones from any pile, they can also be divided into two small piles.

(The number of stones in each heap must not be 0). The winner wins the first one.

Idea: Find the rule after finding the SG function;

SG Function Definition and Method: Click to open the link

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           using namespace std;#define INF 1e8#define eps 1e-8#define LL long long#define maxn 1000001#define PI acos(-1.0)int sg[maxn],vis[maxn];void SG(){sg[0]=0;sg[1]=1;for(int i=2;i<100;i++){memset(vis,0,sizeof(vis));for(int j=i-1;j>=0;j--){vis[sg[j]]=1;}for(int j=1;j