#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <cmath>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pii;
const ll MOD = 1e9 + 7;
map<ll, int> numHas;
ll m;
struct node {
int lN;
int rN;
ll a; //max over range
bool mark;
ll lazy; //need to add each element in v2
node(int l = -1, int r = -1, ll b = 0) : lN(l), rN(r), a(b), mark(false), lazy(0) {};
};
vector<node> st;
void makeLeft(int v) {
if (st[v].lN == -1) st[v].lN = st.size(), st.push_back(node());
}
void makeRight(int v) {
if (st[v].rN == -1) st[v].rN = st.size(), st.push_back(node());
}
void makeChild(int v) {
makeLeft(v);
makeRight(v);
}
void push(int v) {
if (st[v].mark) {
st[v].mark = false;
makeChild(v);
st[st[v].lN].mark = true;
st[st[v].rN].mark = true;
st[st[v].lN].lazy += st[v].lazy;
st[st[v].rN].lazy += st[v].lazy;
st[st[v].lN].a += st[v].lazy;
st[st[v].rN].a += st[v].lazy;
st[v].lazy = 0;
}
}
void upd(int v, ll tl, ll tr, ll x, ll l, ll r) {
//upd adds x from l to r
if (l > r) return;
if (l <= tl && r >= tr) {
st[v].a += x;
st[v].lazy += x;
st[v].mark = true;
return;
}
push(v);
ll mid = (tl + tr) / 2;
if (max(l,tl) <= min(r,mid)) makeLeft(v), upd(st[v].lN, tl, mid, x, max(l, tl), min(r, mid));
if (max(l,mid+1) <= min(r,tr)) makeRight(v), upd(st[v].rN, mid + 1, tr, x, max(l, mid + 1), min(r, tr));
st[v].a = max((st[v].lN != -1 ? st[st[v].lN].a : 0), (st[v].rN != -1 ? st[st[v].rN].a : 0));
}
void update(ll x, int e) {
if (numHas.find(x) != numHas.end()) numHas[x]+=e;
else numHas[x] = e;
upd(0, 0, m, -e * x, x + 1, m);
if (e == 1 && numHas[x] == 1) {
upd(0, 0, m, x, x, x);
}
if (e == -1 && numHas[x] == 0) {
upd(0, 0, m, -x, x, x);
}
}
bool qry() { return st[0].a <= 1; }
void init() { st.push_back(node()); }
bool init(int coinsCount, long long maxCoinSize, long long coins[]) {
m = maxCoinSize;
init();
for (ll i = 0; i < coinsCount; ++i) update(coins[i], 1);
return qry();
}
bool is_happy(int event, int coinsCount, long long coins[]) {
for (ll i = 0; i < coinsCount; ++i) update(coins[i], event);
return qry();
}
//ll main() {
// ios::sync_with_stdio(0);
// cin.tie(0);
//
// long long arr[5] = { 1,2,4,8,16 };
// cout << init(5, 100, arr) << endl;
// ll a1[2] = { 2,8 };
// cout << is_happy(-1, 2, a1) << endl;
// ll a2[3] = { 7,9,2 };
// cout << is_happy(1, 3, a2) << endl;
//
// return 0;
//}
