oj.uz

Submission #368235

# Submission time Handle Problem Language Result Execution time Memory
368235 2021-02-19T19:59:38 Z rqi Asceticism (JOI18_asceticism) C++14
100 / 100
 27 ms 2816 KB 
#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<db,db> pd; 

typedef vector<int> vi; 
typedef vector<bool> vb; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair
#define f first
#define s second
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define sor(x) sort(all(x)) 
#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 trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
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}; 
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

template<class T> bool ckmin(T& a, const T& b) { 
	return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
	return a < b ? a = b, 1 : 0; } 
constexpr int pct(int x) { return __builtin_popcount(x); } 
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
ll half(ll x) { return fdiv(x,2); }

template<class T, class U> T fstTrue(T lo, T hi, U f) { 
	// note: if (lo+hi)/2 is used instead of half(lo+hi) then this will loop infinitely when lo=hi
	hi ++; assert(lo <= hi); // assuming f is increasing
	while (lo < hi) { // find first index such that f is true 
		T mid = half(lo+hi);
		f(mid) ? hi = mid : lo = mid+1; 
	} 
	return lo;
}
template<class T, class U> T lstTrue(T lo, T hi, U f) {
	lo --; assert(lo <= hi); // assuming f is decreasing
	while (lo < hi) { // find first index such that f is true 
		T mid = half(lo+hi+1);
		f(mid) ? lo = mid : hi = mid-1;
	} 
	return lo;
}
template<class T> void remDup(vector<T>& v) { 
	sort(all(v)); v.erase(unique(all(v)),end(v)); }

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) { 
	#ifdef LOCAL
		return b ? "true" : "false"; 
	#else 
		return ts((int)b);
	#endif
}
template<class A> str ts(complex<A> c) { 
	stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
	str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
	res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
	str res = ""; F0R(i,SZ) res += char('0'+b[i]);
	return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
	#ifdef LOCAL
		bool fst = 1; str res = "{";
		for (const auto& x: v) {
			if (!fst) res += ", ";
			fst = 0; res += ts(x);
		}
		res += "}"; return res;
	#else
		bool fst = 1; str res = "";
		for (const auto& x: v) {
			if (!fst) res += " ";
			fst = 0; res += ts(x);
		}
		return res;

	#endif
}
template<class A, class B> str ts(pair<A,B> p) {
	#ifdef LOCAL
		return "("+ts(p.f)+", "+ts(p.s)+")"; 
	#else
		return ts(p.f)+" "+ts(p.s);
	#endif
}

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
	pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
	pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
	cerr << ts(h); if (sizeof...(t)) cerr << ", ";
	DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
	#define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
	#define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
		 << __FUNCTION__  << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
	#define dbg(...) 0
	#define chk(...) 0
#endif

// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
	unsyncIO();
	// 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
}

/**
 * Description: modular arithmetic operations 
 * Source: 
	* KACTL
	* https://codeforces.com/blog/entry/63903
	* https://codeforces.com/contest/1261/submission/65632855 (tourist)
	* https://codeforces.com/contest/1264/submission/66344993 (ksun)
	* also see https://github.com/ecnerwala/cp-book/blob/master/src/modnum.hpp (ecnerwal)
 * Verification: 
	* https://open.kattis.com/problems/modulararithmetic
 */

template<int MOD, int RT> struct mint {
	static const int mod = MOD;
	static constexpr mint rt() { return RT; } // primitive root for FFT
	int v; explicit operator int() const { return v; } // explicit -> don't silently convert to int
	mint() { v = 0; }
	mint(ll _v) { v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
		if (v < 0) v += MOD; }
	friend bool operator==(const mint& a, const mint& b) { 
		return a.v == b.v; }
	friend bool operator!=(const mint& a, const mint& b) { 
		return !(a == b); }
	friend bool operator<(const mint& a, const mint& b) { 
		return a.v < b.v; }
	friend void re(mint& a) { ll x; re(x); a = mint(x); }
	friend str ts(mint a) { return ts(a.v); }
   
	mint& operator+=(const mint& m) { 
		if ((v += m.v) >= MOD) v -= MOD; 
		return *this; }
	mint& operator-=(const mint& m) { 
		if ((v -= m.v) < 0) v += MOD; 
		return *this; }
	mint& operator*=(const mint& m) { 
		v = (ll)v*m.v%MOD; return *this; }
	mint& operator/=(const mint& m) { return (*this) *= inv(m); }
	friend mint pow(mint a, ll p) {
		mint ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans; }
	friend mint inv(const mint& a) { assert(a.v != 0); 
		return pow(a,MOD-2); }
		
	mint operator-() const { return mint(-v); }
	mint& operator++() { return *this += 1; }
	mint& operator--() { return *this -= 1; }
	friend mint operator+(mint a, const mint& b) { return a += b; }
	friend mint operator-(mint a, const mint& b) { return a -= b; }
	friend mint operator*(mint a, const mint& b) { return a *= b; }
	friend mint operator/(mint a, const mint& b) { return a /= b; }
};

typedef mint<MOD,5> mi; // 5 is primitive root for both common mods
typedef vector<mi> vmi;
typedef pair<mi,mi> pmi;
typedef vector<pmi> vpmi;

/**
 * Description: pre-compute factorial mod inverses,
 	* assumes $MOD$ is prime and $SZ < MOD$.
 * Time: O(SZ)
 * Source: KACTL
 * Verification: https://dmoj.ca/problem/tle17c4p5
 */

vi invs, fac, ifac; // make sure to convert to LL before doing any multiplications ...
void genFac(int SZ) {
	invs.rsz(SZ), fac.rsz(SZ), ifac.rsz(SZ); 
	invs[1] = fac[0] = ifac[0] = 1; 
	FOR(i,2,SZ) invs[i] = MOD-(ll)MOD/i*invs[MOD%i]%MOD;
	FOR(i,1,SZ) {
		fac[i] = (ll)fac[i-1]*i%MOD;
		ifac[i] = (ll)ifac[i-1]*invs[i]%MOD;
	}
}

ll comb(int a, int b) {
	if (a < b || b < 0) return 0;
	return (ll)fac[a]*ifac[b]%MOD*ifac[a-b]%MOD;
}

mi getEul(int n, int k){
	mi ans = 0;
	for(int j = 0; j <= k; j++){
		ans+=pow(mi(-1), j)*(pow(mi(k-j), n))*mi(comb(n+1, j));
	}
	return ans;
}


int main() {
	setIO();
	genFac(200005);
	int N, K;
	cin >> N >> K;

	mi ans = getEul(N, K);

	cout << ans.v << "\n";
	// 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
	* WRITE STUFF DOWN
*/

Compilation message

asceticism.cpp: In function 'void setIn(str)':
asceticism.cpp:168:28: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  168 | void setIn(str s) { freopen(s.c_str(),"r",stdin); }
      |                     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
asceticism.cpp: In function 'void setOut(str)':
asceticism.cpp:169:29: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  169 | void setOut(str s) { freopen(s.c_str(),"w",stdout); }
      |                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 2668 KB Output is correct
2 Correct 8 ms 2668 KB Output is correct
3 Correct 8 ms 2668 KB Output is correct
4 Correct 8 ms 2668 KB Output is correct
5 Correct 8 ms 2668 KB Output is correct
6 Correct 8 ms 2668 KB Output is correct
7 Correct 8 ms 2668 KB Output is correct
8 Correct 8 ms 2668 KB Output is correct
9 Correct 9 ms 2668 KB Output is correct
10 Correct 8 ms 2668 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 2668 KB Output is correct
2 Correct 8 ms 2668 KB Output is correct
3 Correct 8 ms 2668 KB Output is correct
4 Correct 8 ms 2668 KB Output is correct
5 Correct 8 ms 2668 KB Output is correct
6 Correct 8 ms 2668 KB Output is correct
7 Correct 8 ms 2668 KB Output is correct
8 Correct 8 ms 2668 KB Output is correct
9 Correct 9 ms 2668 KB Output is correct
10 Correct 8 ms 2668 KB Output is correct
11 Correct 7 ms 2668 KB Output is correct
12 Correct 8 ms 2688 KB Output is correct
13 Correct 8 ms 2668 KB Output is correct
14 Correct 9 ms 2668 KB Output is correct
15 Correct 8 ms 2668 KB Output is correct
16 Correct 8 ms 2668 KB Output is correct
17 Correct 8 ms 2668 KB Output is correct
18 Correct 8 ms 2668 KB Output is correct
19 Correct 9 ms 2668 KB Output is correct
20 Correct 8 ms 2668 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 2668 KB Output is correct
2 Correct 8 ms 2668 KB Output is correct
3 Correct 8 ms 2668 KB Output is correct
4 Correct 8 ms 2668 KB Output is correct
5 Correct 8 ms 2668 KB Output is correct
6 Correct 8 ms 2668 KB Output is correct
7 Correct 8 ms 2668 KB Output is correct
8 Correct 8 ms 2668 KB Output is correct
9 Correct 9 ms 2668 KB Output is correct
10 Correct 8 ms 2668 KB Output is correct
11 Correct 7 ms 2668 KB Output is correct
12 Correct 8 ms 2688 KB Output is correct
13 Correct 8 ms 2668 KB Output is correct
14 Correct 9 ms 2668 KB Output is correct
15 Correct 8 ms 2668 KB Output is correct
16 Correct 8 ms 2668 KB Output is correct
17 Correct 8 ms 2668 KB Output is correct
18 Correct 8 ms 2668 KB Output is correct
19 Correct 9 ms 2668 KB Output is correct
20 Correct 8 ms 2668 KB Output is correct
21 Correct 8 ms 2668 KB Output is correct
22 Correct 8 ms 2668 KB Output is correct
23 Correct 8 ms 2668 KB Output is correct
24 Correct 8 ms 2668 KB Output is correct
25 Correct 8 ms 2668 KB Output is correct
26 Correct 8 ms 2668 KB Output is correct
27 Correct 8 ms 2668 KB Output is correct
28 Correct 8 ms 2668 KB Output is correct
29 Correct 8 ms 2668 KB Output is correct
30 Correct 8 ms 2796 KB Output is correct

Subtask #4
51.0 / 51.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 2668 KB Output is correct
2 Correct 8 ms 2668 KB Output is correct
3 Correct 8 ms 2668 KB Output is correct
4 Correct 8 ms 2668 KB Output is correct
5 Correct 8 ms 2668 KB Output is correct
6 Correct 8 ms 2668 KB Output is correct
7 Correct 8 ms 2668 KB Output is correct
8 Correct 8 ms 2668 KB Output is correct
9 Correct 9 ms 2668 KB Output is correct
10 Correct 8 ms 2668 KB Output is correct
11 Correct 7 ms 2668 KB Output is correct
12 Correct 8 ms 2688 KB Output is correct
13 Correct 8 ms 2668 KB Output is correct
14 Correct 9 ms 2668 KB Output is correct
15 Correct 8 ms 2668 KB Output is correct
16 Correct 8 ms 2668 KB Output is correct
17 Correct 8 ms 2668 KB Output is correct
18 Correct 8 ms 2668 KB Output is correct
19 Correct 9 ms 2668 KB Output is correct
20 Correct 8 ms 2668 KB Output is correct
21 Correct 8 ms 2668 KB Output is correct
22 Correct 8 ms 2668 KB Output is correct
23 Correct 8 ms 2668 KB Output is correct
24 Correct 8 ms 2668 KB Output is correct
25 Correct 8 ms 2668 KB Output is correct
26 Correct 8 ms 2668 KB Output is correct
27 Correct 8 ms 2668 KB Output is correct
28 Correct 8 ms 2668 KB Output is correct
29 Correct 8 ms 2668 KB Output is correct
30 Correct 8 ms 2796 KB Output is correct
31 Correct 8 ms 2668 KB Output is correct
32 Correct 8 ms 2668 KB Output is correct
33 Correct 10 ms 2816 KB Output is correct
34 Correct 11 ms 2668 KB Output is correct
35 Correct 24 ms 2668 KB Output is correct
36 Correct 25 ms 2668 KB Output is correct
37 Correct 27 ms 2668 KB Output is correct
38 Correct 10 ms 2668 KB Output is correct
39 Correct 13 ms 2668 KB Output is correct
40 Correct 16 ms 2668 KB Output is correct