Uoj 33 树上GCD (树分治)

#include 
#include 
#include 
#include 
#include 
#include 
#include 
using namespace std;


#define N 300020
#define B 300
#define M 600200
#define inf 0x3f3f3f3f
#define mod 1000000007
#define LL long long
#define ls (i << 1)
#define rs (ls | 1)
#define md (ll + rr >> 1)
#define lson ll, md, ls
#define rson md + 1, rr, rs
#define MP make_pair
#define ui unsigned int

int n, fa[N];
int fst[N], nxt[M], vv[M], e;
int q[N], qh, qt;
int dep[N], sz[N], mx[N];
LL ans1[N], ans2[N];
bool vis[N];
int rt;
LL x[N], y[N], xx[N], yy[N];
LL F[B + 10][B + 10];


void init() {
	memset(fst, -1, sizeof fst);
	e = 0;
}
void add(int u, int v) {
	vv[e] = v, nxt[e] = fst[u], fst[u] = e++;
}

void bfs(int s, int fd) {
	dep[s] = fd;
	qh = qt = 0;
	q[qt++] = s;
	while(qh < qt) {
		int u = q[qh++];
		for(int i = fst[u]; ~i; i = nxt[i]) {
			int v = vv[i];
			if(vis[v]) continue;
			dep[v] = dep[u] + 1;
			q[qt++] = v;
		}
	}
}

void get_rt(int u) {
	bfs(u, 0);
	for(int i = qt - 1; i >= 0; --i) {
		int u = q[i];
		sz[u] = 1;
		for(int j = fst[u]; ~j; j = nxt[j]) {
			int v = vv[j];
			if(vis[v]) continue;
			sz[u] += sz[v];
		}
	}
	int tmp = n + 1;
	for(int i = 0; i < qt; ++i) {
		int u = q[i];
		mx[u] = 0;
		for(int j = fst[u]; ~j; j = nxt[j]) {
			int v = vv[j];
			if(vis[v]) continue;
			mx[u] = max(mx[u], sz[v]);
		}
		mx[u] = max(mx[u], qt - sz[u]);
		if(mx[u] < tmp) tmp = mx[u], rt = u;
	}
}



void divide(int s) {
	get_rt(s);
	vis[rt] = 1;
	int rrt = rt;
	int tp = 0;

	for(int i = fst[rt]; ~i; i = nxt[i]) {
		int v = vv[i];
		if(vis[v]) continue;
		bfs(v, 1);
		tp = max(tp, qt);
		for(int j = 0; j < qt; ++j) {
			int u = q[j];
			y[dep[u]]++;
			ans2[dep[u]]++;
		}
		for(int j = 1; j <= qt; ++j) {
			x[j] += y[j];
			for(int k = j; k <= qt; k += j) {
				yy[j] += y[k];
			}
		}
		for(int j = 1; j <= qt; ++j) {
			ans1[j] += 1LL * xx[j] * yy[j];
			xx[j] += yy[j];
			yy[j] = y[j] = 0;
		}
	}
	x[0]++;
	int mx_qt = 0;

	int t = 1;
	for(int u = rt; u != s; ++t) {
		u = fa[u];
		bfs(u, 0);
		mx_qt = max(mx_qt, qt);
		for(int i = 1; i < qt; ++i) {
			y[dep[q[i]]]++;
		}
		for(int i = 1; i <= qt; ++i) {
			for(int j = i; j <= qt; j += i)
	
				yy[i] += y[j];
		}
		for(int i = 1; i <= min(qt, B); ++i) {
			if(F[i][t%i] == -1) {
				F[i][t%i] = 0;
				for(int j = (i - t % i) % i; j <= tp; j += i) {
					F[i][t%i] += x[j];
				}
			}
			ans1[i] += F[i][t%i] * yy[i];
		}
		for(int i = B + 1; i <= qt; ++i) {
			for(int j = (i - t % i) % i; j <= tp; j += i)
				ans1[i] += x[j] * yy[i];
		}
		for(int i = 1; i <= qt; ++i) y[i] = yy[i] = 0;
		vis[u] = 1;
	}
	for(int i = 1; i <= min(mx_qt, B); ++i) {
		for(int j = 0; j < i; ++j)
			F[i][j] = -1;
	}
	for(int u = rt; u != s;) {
		u = fa[u];
		vis[u] = 0;
	}

	--t;
	LL tmp = 0;
	for(int k = 1; k <= tp + t; ++k) {
		if(k - 1 <= tp) tmp += x[k-1];
		if(k - t - 1 >= 0 && k - t - 1 <= tp) tmp -= x[k-t-1];
		ans2[k] += tmp;
	}
	for(int i = 0; i <= tp; ++i) x[i] = xx[i] = 0;
	if(rrt != s) divide(s);
	for(int i = fst[rrt]; ~i; i = nxt[i]) {
		int v = vv[i];
		if(!vis[v]) {
			divide(v);
		}
	}
}
int main() {
	scanf("%d", &n);
	init();
	for(int i = 2; i <= n; ++i) {
		scanf("%d", &fa[i]);
		add(fa[i], i);
	}
	memset(F, -1, sizeof F);
	divide(1);
	for(int i = n - 1; i >= 1; --i) {
		for(int j = i + i; j <= n - 1; j += i) {
			ans1[i] -= ans1[j];
		}
	}
	for(int i = 1; i <= n - 1; ++i) {
		printf("%lld\n", ans1[i] + ans2[i]);
	}
	return 0;
}