text: #include <bits/stdc++.h>
  using namespace std;
   
  typedef long long ll;
  typedef long double ld;
  typedef double db; 
  typedef string str; 
  
  typedef pair<int,int> pi;
  typedef pair<ll,ll> pl; 
  typedef pair<ld,ld> pd; 
  #define mp make_pair
  #define f first
  #define s second
  
  typedef vector<int> vi; 
  typedef vector<ll> vl; 
  typedef vector<ld> vd; 
  typedef vector<str> vs; 
  typedef vector<pi> vpi;
  typedef vector<pl> vpl; 
  typedef vector<pd> vpd; 
  
  #define sz(x) (int)x.size()
  #define all(x) begin(x), end(x)
  #define rall(x) (x).rbegin(), (x).rend() 
  #define rsz resize
  #define ins insert 
  #define ft front() 
  #define bk back()
  #define pf push_front 
  #define pb push_back
  #define eb emplace_back 
  #define lb lower_bound 
  #define ub upper_bound 
  
  #define FOR(i,a,b) for (int i = (a); i < (b); ++i)
  #define F0R(i,a) FOR(i,0,a)
  #define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
  #define R0F(i,a) ROF(i,0,a)
  #define each(a,x) for (auto& a: x)
  
  const int MOD = 1e9+7; // 998244353; // = (119<<23)+1
  const int MX = 2e5+5;
  const ll INF = 1e18; 
  const ld PI = acos((ld)-1);
  const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 
  
  template<class T> bool ckmin(T& a, const T& b) { 
  	return a > b ? a = b, 1 : 0; }
  template<class T> bool ckmax(T& a, const T& b) { 
  	return a < b ? a = b, 1 : 0; }
  int pc(int x) { return __builtin_popcount(x); } 
  
  #include <ext/pb_ds/tree_policy.hpp>
  #include <ext/pb_ds/assoc_container.hpp>
  using namespace __gnu_pbds;
  template <class T> using Tree = tree<T, null_type, less<T>, 
  	rb_tree_tag, tree_order_statistics_node_update>; 
  // change null_type for map
  #define ook order_of_key
  #define fbo find_by_order
  
  void treeExample() {
  	Tree<int> t, t2; t.insert(8);
  	auto it = t.insert(10).f; assert(it == t.lb(9));
  	assert(t.ook(10) == 1); assert(t.ook(11) == 2);
  	assert(*t.fbo(0) == 8);
  	t.join(t2); // assuming T < T2 or T > T2, merge t2 into t
  }
  
  namespace input {
  	template<class T> void re(complex<T>& x);
  	template<class T1, class T2> void re(pair<T1,T2>& p);
  	template<class T> void re(vector<T>& a);
  	template<class T, size_t SZ> void re(array<T,SZ>& a);
  
  	template<class T> void re(T& x) { cin >> x; }
  	void re(double& x) { string t; re(t); x = stod(t); }
  	void re(ld& x) { string t; re(t); x = stold(t); }
  	template<class T, class... Ts> void re(T& t, Ts&... ts) { 
  		re(t); re(ts...); 
  	}
  
  	template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
  	template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
  	template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
  	template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
  }
  
  using namespace input;
  
  namespace output {
  	void pr(int x) { cout << x; }
  	void pr(long x) { cout << x; }
  	void pr(ll x) { cout << x; }
  	void pr(unsigned x) { cout << x; }
  	void pr(unsigned long x) { cout << x; }
  	void pr(unsigned long long x) { cout << x; }
  	void pr(float x) { cout << x; }
  	void pr(double x) { cout << x; }
  	void pr(ld x) { cout << x; }
  	void pr(char x) { cout << x; }
  	void pr(const char* x) { cout << x; }
  	void pr(const string& x) { cout << x; }
  	void pr(bool x) { pr(x ? "true" : "false"); }
  	template<class T> void pr(const complex<T>& x) { cout << x; }
  	
  	template<class T1, class T2> void pr(const pair<T1,T2>& x);
  	template<class T> void pr(const T& x);
  	
  	template<class T, class... Ts> void pr(const T& t, const Ts&... ts) { 
  		pr(t); pr(ts...); 
  	}
  	template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
  		pr("{",x.f,", ",x.s,"}"); 
  	}
  	template<class T> void pr(const T& x) { 
  		pr("{"); // const iterator needed for vector<bool>
  		bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; 
  		pr("}");
  	}
  	
  	void ps() { pr("\n"); } // print w/ spaces
  	template<class T, class... Ts> void ps(const T& t, const Ts&... ts) { 
  		pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); 
  	}
  	
  	void pc() { pr("]\n"); } // debug w/ commas
  	template<class T, class... Ts> void pc(const T& t, const Ts&... ts) { 
  		pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); 
  	}
  	#define dbg(x...) pr("[",#x,"] = ["), pc(x);
  }
  
  using namespace output;
  
  namespace io {
  	void setIn(string s) { freopen(s.c_str(),"r",stdin); }
  	void setOut(string s) { freopen(s.c_str(),"w",stdout); }
  	void setIO(string s = "") {
  		ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
  		// cin.exceptions(cin.failbit); 
  		// throws exception when do smth illegal
  		// ex. try to read letter into int
  		if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
  	}
  }
  
  using namespace io;
  
  struct mi {
  	typedef decay<decltype(MOD)>::type T; 
   	/// don't silently convert to T
  	T v; explicit operator T() const { return v; }
  	mi() { v = 0; }
  	mi(ll _v) { 
  		v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
  		if (v < 0) v += MOD;
  	}
  	friend bool operator==(const mi& a, const mi& b) { 
  		return a.v == b.v; }
  	friend bool operator!=(const mi& a, const mi& b) { 
  		return !(a == b); }
  	friend bool operator<(const mi& a, const mi& b) { 
  		return a.v < b.v; }
  	friend void re(mi& a) { ll x; re(x); a = mi(x); }
  	friend void pr(const mi& a) { pr(a.v); }
  	friend ostream& operator<<(ostream& os, const mi& a) { 
  		return os << a.v; }
     
  	mi& operator+=(const mi& m) { 
  		if ((v += m.v) >= MOD) v -= MOD; 
  		return *this; }
  	mi& operator-=(const mi& m) { 
  		if ((v -= m.v) < 0) v += MOD; 
  		return *this; }
  	mi& operator*=(const mi& m) { 
  		v = (ll)v*m.v%MOD; return *this; }
  	mi& operator/=(const mi& m) { return (*this) *= inv(m); }
  	friend mi pow(mi a, ll p) {
  		mi ans = 1; assert(p >= 0);
  		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
  		return ans;
  	}
  	friend mi inv(const mi& a) { assert(a.v != 0); 
  		return pow(a,MOD-2); }
  		
  	mi operator-() const { return mi(-v); }
  	mi& operator++() { return *this += 1; }
  	mi& operator--() { return *this -= 1; }
  	friend mi operator+(mi a, const mi& b) { return a += b; }
  	friend mi operator-(mi a, const mi& b) { return a -= b; }
  	friend mi operator*(mi a, const mi& b) { return a *= b; }
  	friend mi operator/(mi a, const mi& b) { return a /= b; }
  };
  typedef vector<mi> vmi;
  typedef pair<mi,mi> pmi;
  typedef vector<pmi> vpmi;
  
  vector<vmi> comb;
  void genComb(int SZ) {
  	comb.assign(SZ,vmi(SZ)); comb[0][0] = 1;
  	FOR(i,1,SZ) F0R(j,i+1) 
  		comb[i][j] = comb[i-1][j]+(j?comb[i-1][j-1]:0);
  }
  
  mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 
  
  /**
   * Description: custom bitset
   * Source: Own
   	* Also see https://www.hackerrank.com/contests/noi-ph-2019-finals-1/challenges/sumbong-centers/editorial
   * Verification: see bset.cpp
   */
  
  struct bset {
  	typedef uint64_t ul;
  	int size; vector<ul> b; 
  	bset(int x) : size(x), b((x+63)/64) {}
  	bool get(int x) const { return (b[x/64]>>(x%64))&1; }
  	void flip(int x) { b[x/64] ^= (ul)1<<(x%64); }
  	void set(int x) { if (!get(x)) flip(x); }
  	int count() {
  		int res = 0; each(t,b) res += __builtin_popcountll(t);
  		return res;
  	}
  	friend void pr(const bset& x) { F0R(i,x.size) pr((int)x.get(i)); }
  	bset& operator|=(const bset& r) {
  		assert(size == r.size); F0R(i,sz(b)) b[i] |= r.b[i]; }
  	bset& operator&=(const bset& r) {
  		assert(size == r.size); F0R(i,sz(b)) b[i] &= r.b[i]; }
  	bset shift(int inc) { // cyclic shift b to right
  		inc %= size; if (inc < 0) inc += size;
  		bset res(size);
  		int r0 = inc/64, r1 = inc%64;
  		int l0 = (size-inc)/64, l1 = (size-inc)%64;
  		F0R(i,sz(b)-r0) {
  			res.b[i+r0] |= b[i]<<r1;
  			if (r1 && i+r0+1 < sz(b)) 
  				res.b[i+r0+1] |= b[i]>>(64-r1);
  		}
  		FOR(i,l0,sz(b)) {
  			res.b[i-l0] |= b[i]>>l1;
  			if (l1 && i >= l0+1) 
  				res.b[i-l0-1] |= b[i]<<(64-l1);
  		}
  		int rem = size%64; if (rem) res.b.bk &= ((ul)1<<rem)-1;
  		return res;
  	}
  	int findNext(int x) { // first bit after x
  		int i = x < 0 ? -1 : x/64, p = (x+1)%64;
  		if (p != 0) {
  			ul a = b[i]; a ^= a&(((ul)1<<p)-1);
  			int t = __builtin_ffsll(a);
  			if (t) return 64*i+t-1;
  		}
  		while (++i < sz(b)) {
  			int t = __builtin_ffsll(b[i]);
  			if (t) return 64*i+t-1;
  		}
  		return size;
  	}
  };
  
  int main() { 
  	// ios_base::sync_with_stdio(0); cin.tie(0); 
  	F0R(i,1000) {
  		int sz = rand()%1000+1;
  		bset t(sz);
  		vector<bool> b; F0R(j,sz) b.pb(rand()&1);
  		// ps("??",sz,sz(b));
  		int num = 0;
  		F0R(i,sz(b)) if (b[i]) {
  			t.set(i);
  			num ++;
  			// ps("FLIP",i);
  			//ps(t.get(i));
  			//exit(0);
  		}
  		int inc = rand()%sz;
  		auto T = t.shift(inc);
  		F0R(j,sz) if (b[j] != T.get((j+inc)%sz)) {
  			// ps("OOPS",j,(bool)b[j],T.get((j+inc)%sz));
  			pr(t); ps(); pr(T);
  			exit(0);
  		}
  		assert(num == T.count());
  
  	}
  	F0R(i,1000) {
  		int sz = rand()%1000+1;
  		bset t(sz);
  		set<int> ok;
  		F0R(j,rand()%20+1) {
  			int pos = rand()%sz;
  			t.set(pos);
  			ok.insert(pos);
  		}
  		int a = -1;
  		set<int> OK;
  		while (a != t.size) {
  			OK.insert(a);
  			int A = a;
  			a = t.findNext(a);
  			if (a == A) {
  				ps("WHOOPS",a);
  				exit(0);
  			}
  			//ps("HA",a);
  		}
  		OK.erase(-1);
  		assert(ok == OK);
  		/*int pos = rand()%sz;
  		t.set(pos);
  		//ps(t.get(64));
  		if (pos != t.findFirst()) {
  			ps("AH",sz,pos,t.findFirst());
  			exit(0);
  		}
  		assert(pos == t.findFirst());*/
  	}
  	//ps(ffs(0),ffs(1),ffs(2),ffs(3));
  	//uint64_t u; u += ((uint64_t)1<<63)+(uint64_t)(1<<5);
  	//ps((ll)u,__builtin_ffsll(u));
  	ps("OK");
  	// you should actually read the stuff at the bottom
  }
  
  /* stuff you should look for
  	* int overflow, array bounds
  	* special cases (n=1?)
  	* do smth instead of nothing and stay organized
  */
  