Codeforces 548E（莫反、容斥）

转化为质数域上的操作，如果用莫反的话，记录因数的cnt。
其实莫反的推式子最后和容斥做法殊途同归了，容斥的系数就是莫比乌斯函数。

const int maxn = 2e5 + 5, maxa = 5e5 + 5;

int n, q, a[maxn], maxx;
int primes[maxa], tot, vis[maxa], mu[maxa];
vector<int> fac[maxa];

ll ans;
int g[maxa];
bool mark[maxn];

void Pre() {
	mu[1] = 1;
	for (int i = 2; i <= maxx; i++) {
		if (!vis[i]) {
			primes[++tot] = i;
			mu[i] = -1;
		}
		for (int j = 1; j <= tot && (ll)primes[j] * i <= maxx; j++) {
			vis[primes[j] * i] = 1;
			if (i % primes[j] == 0)	break;
			mu[primes[j] * i] = -mu[i];
		}
	}5
	for (int i = 1; i <= maxx; i++)
		for (int j = 1; (ll)j * i <= maxx; j++)
			fac[j * i].push_back(i);
}

int main() {	
	read(n), read(q);
	rep(i, 1, n)	read(a[i]), maxx = max(maxx, a[i]);
	Pre();
	for (int i; q; q--) {
		read(i);
		if (!mark[i]) {
			mark[i] = 1;
			for (int d : fac[a[i]]) {
				ans += mu[d] * g[d];
				g[d]++;
			}
		} else {
			mark[i] = 0;
			for (int d : fac[a[i]]) {
				g[d]--;
				ans -= mu[d] * g[d];
			}
		}
		writeln(ans);
	}
	return 0;
}