#839699 (C++14) No.2215 Slide Subset Sum

• 問題: No.2215 Slide Subset Sum
• ユーザー: woodywoody
• 提出日時: 2023-02-12 03:28:58
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 878 ms / 3,000 ms
• コード長: 18,449 bytes
• コンパイル時間: 4,246 ms
• コンパイル使用メモリ: 245,068 KB
• 実行使用メモリ: 176,384 KB
• 最終ジャッジ日時: 2024-07-08 12:44:59
• 合計ジャッジ時間: 24,574 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	343 ms; 5,248 KB
testcase_01	AC	876 ms; 5,376 KB
testcase_02	AC	870 ms; 5,460 KB
testcase_03	AC	872 ms; 5,416 KB
testcase_04	AC	867 ms; 8,704 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	1 ms; 5,376 KB
testcase_16	AC	3 ms; 5,376 KB
testcase_17	AC	809 ms; 82,432 KB
testcase_18	AC	772 ms; 71,340 KB
testcase_19	AC	878 ms; 7,416 KB
testcase_20	AC	667 ms; 91,260 KB
testcase_21	AC	851 ms; 24,656 KB
testcase_22	AC	689 ms; 97,792 KB
testcase_23	AC	703 ms; 158,720 KB
testcase_24	AC	704 ms; 159,488 KB
testcase_25	AC	692 ms; 141,948 KB
testcase_26	AC	675 ms; 98,432 KB
testcase_27	AC	38 ms; 5,376 KB
testcase_28	AC	35 ms; 9,344 KB
testcase_29	AC	54 ms; 7,168 KB
testcase_30	AC	404 ms; 5,376 KB
testcase_31	AC	235 ms; 61,184 KB
testcase_32	AC	69 ms; 5,632 KB
testcase_33	AC	540 ms; 17,604 KB
testcase_34	AC	425 ms; 44,288 KB
testcase_35	AC	105 ms; 5,376 KB
testcase_36	AC	137 ms; 28,928 KB
testcase_37	AC	420 ms; 176,384 KB
testcase_38	AC	61 ms; 26,368 KB
testcase_39	AC	877 ms; 5,376 KB
testcase_40	AC	274 ms; 5,376 KB
testcase_41	AC	2 ms; 5,376 KB
testcase_42	AC	678 ms; 91,000 KB
testcase_43	AC	663 ms; 13,764 KB
testcase_44	AC	663 ms; 13,892 KB
testcase_45	AC	705 ms; 133,760 KB
testcase_46	AC	698 ms; 133,760 KB

ソースコード

#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,b) for(int i=0;i<b;i++)
#define rrep(i,b) for(int i=b-1;i>=0;i--)
#define rep1(i,b) for(int i=1;i<b;i++)
#define repx(i,x,b) for(int i=x;i<b;i++)
#define rrepx(i,x,b) for(int i=b-1;i>=x;i--)
#define fore(i,a) for(auto i:a)
#define fore1(i,a) for(auto &i:a)
#define rng(x) (x).begin(), (x).end()
#define rrng(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define fi first
#define se second
#define pcnt __builtin_popcountll

using namespace std;
using namespace atcoder;

using ll = long long;
using ld = long double;
template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}}
#define dame { cout << "No" << endl; return;}
#define dame1 { cout << -1 << endl; return;}
#define cout2(x,y) cout << x << " " << y << endl;
#define coutp(p) cout << p.fi << " " << p.se << endl;
#define out cout << ans << endl;
#define outd cout << fixed << setprecision(20) << ans << endl;
#define outm cout << ans.val() << endl;
#define outv fore(yans , ans) cout << yans << "\n";
#define outdv fore(yans , ans) cout << yans.val() << "\n";
#define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define coutv2(v) fore(vy , v) cout << vy << "\n";
#define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define coutvm2(v) fore(vy , v) cout << vy.val() << "\n";
using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;using pii = pair<int,int>;using pdd = pair<ld,ld>;
using tp = tuple<int ,int ,int>;
using vi = vector<int>;using vd = vector<ld>;using vl = vector<ll>;using vs = vector<string>;using vb = vector<bool>;
using vpii = vector<pii>;using vpli = vector<pli>;using vpll = vector<pll>;using vpil = vector<pil>;
using vvi = vector<vector<int>>;using vvl = vector<vector<ll>>;using vvs = vector<vector<string>>;using vvb = vector<vector<bool>>;
using vvpii = vector<vector<pii>>;using vvpli = vector<vector<pli>>;using vvpll = vector<vpll>;using vvpil = vector<vpil>;
using mint = modint998244353;
//using mint = modint1000000007;
//using mint = dynamic_modint<0>;
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};
ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}
#define yes {cout <<"Yes"<<endl;}
#define yesr { cout <<"Yes"<<endl; return;}
#define no {cout <<"No"<<endl;}
#define nor { cout <<"No"<<endl; return;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#ifdef MY_LOCAL_DEBUG
#define show(x) cerr<<#x<<" = "<<x<<endl
#define showp(p) cerr<<#p<<" = "<<p.fi<<" : "<<p.se<<endl
#define show2(x,y) cerr<<#x<<" = "<<x<<" : "<<#y<<" = "<<y<<endl
#define show3(x,y,z) cerr<<#x<<" = "<<x<<" : "<<#y<<" = "<<y<<" : "<<#z<<" = "<<z<<endl
#define show4(x,y,z,x2) cerr<<#x<<" = "<<x<<" : "<<#y<<" = "<<y<<" : "<<#z<<" = "<<z<<" : "<<#x2<<" = "<<x2<<endl
#define test(x) cout << "test" << x << endl
#define showv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define showv2(v) fore(vy , v) cout << vy << "\n";
#define showvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define showvm2(v) fore(vy , v) cout << vy.val() << "\n";
#else
#define show(x)
#define showp(p)
#define show2(x,y)
#define show3(x,y,z)
#define show4(x,y,z,x2)
#define test(x)
#define showv(v)
#define showv2(v)
#define showvm(v)
#define showvm2(v)
#endif

struct NTT
{
	uint32_t get_pr()
	{
		uint32_t _mod = mint::mod();
		using u64 = uint64_t;
		u64 ds[32] = {};
		int idx = 0;
		u64 m = _mod - 1;
		for (u64 i = 2; i * i <= m; ++i)
		{
			if (m % i == 0)
			{
				ds[idx++] = i;
				while (m % i == 0)
					m /= i;
			}
		}
		if (m != 1)
			ds[idx++] = m;
	
		uint32_t _pr = 2;
		while (1)
		{
			int flg = 1;
			for (int i = 0; i < idx; ++i)
			{
				u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
				while (b)
				{
					if (b & 1)
						r = r * a % _mod;
					a = a * a % _mod;
					b >>= 1;
				}
				if (r == 1)
				{
					flg = 0;
					break;
				}
			}
			if (flg == 1)
				break;
			++_pr;
		}
		return _pr;
	};
	static constexpr uint32_t mod = mint::mod();
	uint32_t pr = get_pr();
	static constexpr int level = __builtin_ctzll(mod - 1);
	mint dw[level], dy[level];
	void setwy(int k)
	{
		mint w[level], y[level];
		w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
		y[k - 1] = w[k - 1].inv();
		for (int i = k - 2; i > 0; --i)
			w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
		dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
		for (int i = 3; i < k; ++i)
		{
			dw[i] = dw[i - 1] * y[i - 2] * w[i];
			dy[i] = dy[i - 1] * w[i - 2] * y[i];
		}
	}
	NTT() { setwy(level); }
	void fft4(vector<mint> &a, int k)
	{
		if ((int)a.size() <= 1)
			return;
		if (k == 1)
		{
			mint a1 = a[1];
			a[1] = a[0] - a[1];
			a[0] = a[0] + a1;
			return;
		}
		if (k & 1)
		{
			int v = 1 << (k - 1);
			for (int j = 0; j < v; ++j)
			{
				mint ajv = a[j + v];
				a[j + v] = a[j] - ajv;
				a[j] += ajv;
			}
		}
		int u = 1 << (2 + (k & 1));
		int v = 1 << (k - 2 - (k & 1));
		mint one = mint(1);
		mint imag = dw[1];
		while (v)
		{
			// jh = 0
			{
				int j0 = 0;
				int j1 = v;
				int j2 = j1 + v;
				int j3 = j2 + v;
				for (; j0 < v; ++j0, ++j1, ++j2, ++j3)
				{
					mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
					mint t0p2 = t0 + t2, t1p3 = t1 + t3;
					mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
					a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
					a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
				}
			}
			// jh >= 1
			mint ww = one, xx = one * dw[2], wx = one;
			for (int jh = 4; jh < u;)
			{
				ww = xx * xx, wx = ww * xx;
				int j0 = jh * v;
				int je = j0 + v;
				int j2 = je + v;
				for (; j0 < je; ++j0, ++j2)
				{
					mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
						 t3 = a[j2 + v] * wx;
					mint t0p2 = t0 + t2, t1p3 = t1 + t3;
					mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
					a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
					a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
				}
				xx *= dw[__builtin_ctzll((jh += 4))];
			}
			u <<= 2;
			v >>= 2;
		}
	}
	void ifft4(vector<mint> &a, int k)
	{
		if ((int)a.size() <= 1)
			return;
		if (k == 1)
		{
			mint a1 = a[1];
			a[1] = a[0] - a[1];
			a[0] = a[0] + a1;
			return;
		}
		int u = 1 << (k - 2);
		int v = 1;
		mint one = mint(1);
		mint imag = dy[1];
		while (u)
		{
			// jh = 0
			{
				int j0 = 0;
				int j1 = v;
				int j2 = v + v;
				int j3 = j2 + v;
				for (; j0 < v; ++j0, ++j1, ++j2, ++j3)
				{
					mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
					mint t0p1 = t0 + t1, t2p3 = t2 + t3;
					mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
					a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
					a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
				}
			}
			// jh >= 1
			mint ww = one, xx = one * dy[2], yy = one;
			u <<= 2;
			for (int jh = 4; jh < u;)
			{
				ww = xx * xx, yy = xx * imag;
				int j0 = jh * v;
				int je = j0 + v;
				int j2 = je + v;
				for (; j0 < je; ++j0, ++j2)
				{
					mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
					mint t0p1 = t0 + t1, t2p3 = t2 + t3;
					mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
					a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
					a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
				}
				xx *= dy[__builtin_ctzll(jh += 4)];
			}
			u >>= 4;
			v <<= 2;
		}
		if (k & 1)
		{
			u = 1 << (k - 1);
			for (int j = 0; j < u; ++j)
			{
				mint ajv = a[j] - a[j + u];
				a[j] += a[j + u];
				a[j + u] = ajv;
			}
		}
	}
	void ntt(vector<mint> &a)
	{
		if ((int)a.size() <= 1)
			return;
		fft4(a, __builtin_ctz(a.size()));
	}
	void intt(vector<mint> &a)
	{
		if ((int)a.size() <= 1)
			return;
		ifft4(a, __builtin_ctz(a.size()));
		mint iv = mint(a.size()).inv();
		for (auto &x : a)
			x *= iv;
	}
	vector<mint> multiply(const vector<mint> &a, const vector<mint> &b)
	{
		int l = a.size() + b.size() - 1;
		if (min<int>(a.size(), b.size()) <= 40)
		{
			vector<mint> s(l);
			for (int i = 0; i < (int)a.size(); ++i)
				for (int j = 0; j < (int)b.size(); ++j)
					s[i + j] += a[i] * b[j];
			return s;
		}
		int k = 2, M = 4;
		while (M < l)
			M <<= 1, ++k;
		setwy(k);
		vector<mint> s(M), t(M);
		for (int i = 0; i < (int)a.size(); ++i)
			s[i] = a[i];
		for (int i = 0; i < (int)b.size(); ++i)
			t[i] = b[i];
		fft4(s, k);
		fft4(t, k);
		for (int i = 0; i < M; ++i)
			s[i] *= t[i];
		ifft4(s, k);
		s.resize(l);
		mint invm = mint(M).inv();
		for (int i = 0; i < l; ++i)
			s[i] *= invm;
		return s;
	}
	void ntt_doubling(vector<mint> &a)
	{
		int M = (int)a.size();
		auto b = a;
		intt(b);
		mint r = 1, zeta = mint(pr).pow((mint::mod() - 1) / (M << 1));
		for (int i = 0; i < M; i++)
			b[i] *= r, r *= zeta;
		ntt(b);
		copy(begin(b), end(b), back_inserter(a));
	}
};

struct FPS : vector<mint>
{
	using vector<mint>::vector;
	FPS &operator+=(const FPS &r)
	{
		if (r.size() > this->size())
			this->resize(r.size());
		for (int i = 0; i < (int)r.size(); i++)
			(*this)[i] += r[i];
		return *this;
	}
	FPS &operator+=(const mint &r)
	{
		if (this->empty())
			this->resize(1);
		(*this)[0] += r;
		return *this;
	}
	FPS &operator-=(const FPS &r)
	{
		if (r.size() > this->size())
			this->resize(r.size());
		for (int i = 0; i < (int)r.size(); i++)
			(*this)[i] -= r[i];
		return *this;
	}
	FPS &operator-=(const mint &r)
	{
		if (this->empty())
			this->resize(1);
		(*this)[0] -= r;
		return *this;
	}
	FPS &operator*=(const mint &v)
	{
		for (int k = 0; k < (int)this->size(); k++)
			(*this)[k] *= v;
		return *this;
	}
	FPS &operator/=(const FPS &r)
	{
		if (this->size() < r.size())
		{
			this->clear();
			return *this;
		}
		int n = this->size() - r.size() + 1;
		if ((int)r.size() <= 64)
		{
			FPS f(*this), g(r);
			g.shrink();
			mint coeff = g.back().inv();
			for (auto &x : g)
				x *= coeff;
			int deg = (int)f.size() - (int)g.size() + 1;
			int gs = g.size();
			FPS quo(deg);
			for (int i = deg - 1; i >= 0; i--)
			{
				quo[i] = f[i + gs - 1];
				for (int j = 0; j < gs; j++)
					f[i + j] -= quo[i] * g[j];
			}
			*this = quo * coeff;
			this->resize(n, mint(0));
			return *this;
		}
		return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
	}
	FPS &operator%=(const FPS &r)
	{
		*this -= *this / r * r;
		shrink();
		return *this;
	}
	FPS operator+(const FPS &r) const { return FPS(*this) += r; }
	FPS operator+(const mint &v) const { return FPS(*this) += v; }
	FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
	FPS operator-(const mint &v) const { return FPS(*this) -= v; }
	FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
	FPS operator*(const mint &v) const { return FPS(*this) *= v; }
	FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
	FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
	FPS operator-() const
	{
		FPS ret(this->size());
		for (int i = 0; i < (int)this->size(); i++)
			ret[i] = -(*this)[i];
		return ret;
	}
	void shrink()
	{
		while (this->size() && this->back() == mint(0))
			this->pop_back();
	}
	FPS rev() const
	{
		FPS ret(*this);
		reverse(rng(ret));
		return ret;
	}
	FPS dot(FPS r) const
	{
		FPS ret(min(this->size(), r.size()));
		for (int i = 0; i < (int)ret.size(); i++)
			ret[i] = (*this)[i] * r[i];
		return ret;
	}
	FPS pre(int sz) const
	{
		return FPS((*this).begin(), (*this).begin() + min((int)this->size(), sz));
	}
	FPS operator>>(int sz) const
	{
		if ((int)this->size() <= sz)
			return {};
		FPS ret(*this);
		ret.erase(ret.begin(), ret.begin() + sz);
		return ret;
	}
	FPS operator<<(int sz) const
	{
		FPS ret(*this);
		ret.insert(ret.begin(), sz, mint(0));
		return ret;
	}
	FPS diff() const
	{
		const int n = (int)this->size();
		FPS ret(max(0, n - 1));
		mint one(1), coeff(1);
		for (int i = 1; i < n; i++)
		{
			ret[i - 1] = (*this)[i] * coeff;
			coeff += one;
		}
		return ret;
	}
	FPS integral() const
	{
		const int n = (int)this->size();
		FPS ret(n + 1);
		ret[0] = mint(0);
		if (n > 0)
			ret[1] = mint(1);
		auto mod = mint::mod();
		for (int i = 2; i <= n; i++)
			ret[i] = (-ret[mod % i]) * (mod / i);
		for (int i = 0; i < n; i++)
			ret[i + 1] *= (*this)[i];
		return ret;
	}
	mint eval(mint x) const
	{
		mint r = 0, w = 1;
		for (auto &v : *this)
			r += w * v, w *= x;
		return r;
	}
	FPS log(int deg = -1) const
	{
		assert((*this)[0] == mint(1));
		if (deg == -1)
			deg = (int)this->size();
		return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
	}
	FPS pow(int64_t k, int deg = -1) const
	{
		const int n = (int)this->size();
		if (deg == -1)
			deg = n;
		if (k == 0)
		{
			FPS ret(deg);
			if (deg)
				ret[0] = 1;
			return ret;
		}
		for (int i = 0; i < n; i++)
		{
			if ((*this)[i] != mint(0))
			{
				mint rev = mint(1) / (*this)[i];
				FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
				ret *= (*this)[i].pow(k);
				ret = (ret << (i * k)).pre(deg);
				if ((int)ret.size() < deg)
					ret.resize(deg, mint(0));
				return ret;
			}
			if (__int128_t(i + 1) * k >= deg)
				return FPS(deg, mint(0));
		}
		return FPS(deg, mint(0));
	}
	static void *ntt_ptr;
	void set_fft()
	{
		if (!ntt_ptr)
			ntt_ptr = new NTT;
	}
	FPS &operator*=(
		const FPS &r)
	{
		if (this->empty() || r.empty())
		{
			this->clear();
			return *this;
		}
		set_fft();
		auto ret = static_cast<NTT *>(ntt_ptr)->multiply(*this, r);
		return *this = FPS(ret.begin(), ret.end());
	}
	void ntt()
	{
		set_fft();
		static_cast<NTT *>(ntt_ptr)->ntt(*this);
	}
	void intt()
	{
		set_fft();
		static_cast<NTT *>(ntt_ptr)->intt(*this);
	}
	void ntt_doubling()
	{
		set_fft();
		static_cast<NTT *>(ntt_ptr)->ntt_doubling(*this);
	}
	int ntt_pr()
	{
		set_fft();
		return static_cast<NTT *>(ntt_ptr)->pr;
	}
	FPS inv(int deg) const
	{
		assert((*this)[0] != mint(0));
		if (deg == -1)
			deg = (int)this->size();
		FPS res(deg);
		res[0] = {mint(1) / (*this)[0]};
		for (int d = 1; d < deg; d <<= 1)
		{
			FPS f(2 * d), g(2 * d);
			for (int j = 0; j < min((int)this->size(), 2 * d); j++)
				f[j] = (*this)[j];
			for (int j = 0; j < d; j++)
				g[j] = res[j];
			f.ntt();
			g.ntt();
			for (int j = 0; j < 2 * d; j++)
				f[j] *= g[j];
			f.intt();
			for (int j = 0; j < d; j++)
				f[j] = 0;
			f.ntt();
			for (int j = 0; j < 2 * d; j++)
				f[j] *= g[j];
			f.intt();
			for (int j = d; j < min(2 * d, deg); j++)
				res[j] = -f[j];
		}
		return res.pre(deg);
	}
	FPS exp(int deg) const
	{
		using fps = FPS;
		assert((*this).size() == 0 || (*this)[0] == mint(0));
		if (deg == -1)
			deg = this->size();
	
		fps inv;
		inv.reserve(deg + 1);
		inv.push_back(mint(0));
		inv.push_back(mint(1));
	
		auto inplace_integral = [&](fps &F) -> void
		{
			const int n = (int)F.size();
			auto mod = mint::mod();
			while ((int)inv.size() <= n)
			{
				int i = inv.size();
				inv.push_back((-inv[mod % i]) * (mod / i));
			}
			F.insert(F.begin(), mint(0));
			for (int i = 1; i <= n; i++)
				F[i] *= inv[i];
		};
		
		auto inplace_diff = [](fps &F) -> void
		{
			if (F.empty())
				return;
			F.erase(F.begin());
			mint coeff = 1, one = 1;
			for (int i = 0; i < (int)F.size(); i++)
			{
				F[i] *= coeff;
				coeff += one;
			}
		};
		
		fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
		for (int m = 2; m < deg; m *= 2)
		{
			auto y = b;
			y.resize(2 * m);
			y.ntt();
			z1 = z2;
			fps z(m);
			for (int i = 0; i < m; ++i)
				z[i] = y[i] * z1[i];
			z.intt();
			fill(z.begin(), z.begin() + m / 2, mint(0));
			z.ntt();
			for (int i = 0; i < m; ++i)
				z[i] *= -z1[i];
			z.intt();
			c.insert(c.end(), z.begin() + m / 2, z.end());
			z2 = c;
			z2.resize(2 * m);
			z2.ntt();
			fps x((*this).begin(), (*this).begin() + min<int>(this->size(), m));
			x.resize(m);
			inplace_diff(x);
			x.push_back(mint(0));
			x.ntt();
			for (int i = 0; i < m; ++i)
				x[i] *= y[i];
			x.intt();
			x -= b.diff();
			x.resize(2 * m);
			for (int i = 0; i < m - 1; ++i)
				x[m + i] = x[i], x[i] = mint(0);
			x.ntt();
			for (int i = 0; i < 2 * m; ++i)
				x[i] *= z2[i];
			x.intt();
			x.pop_back();
			inplace_integral(x);
			for (int i = m; i < min<int>(this->size(), 2 * m); ++i)
				x[i] += (*this)[i];
			fill(x.begin(), x.begin() + m, mint(0));
			x.ntt();
			for (int i = 0; i < 2 * m; ++i)
				x[i] *= y[i];
			x.intt();
			b.insert(b.end(), x.begin() + m, x.end());
		}
		return fps{b.begin(), b.begin() + deg};
	}
};
void *FPS::ntt_ptr = nullptr;

//FPSライブラリ
//除算 : f/g は右式のqを返す f = g*q + r
//pow(int64_t k, int deg = -1) : f^k mod x^deg
int n,m,k;

template<typename T, T (*op)(const T&,const T&), T (*id)()>
struct swag{
	using ptt = pair<T,T>;
	using st = stack<ptt>;
	st back,front;

	swag(){
		back.push({id(),id()});
		front.push({id(),id()});
	}

	void push(T x){
		front.push({x,op(front.top().se,x)});
	}
	void pop(){
		if (sz(back)==1){
			while(sz(front)>1){
				back.push({front.top().fi,op(back.top().se,front.top().fi)});
				front.pop();
			}
		}
		if (sz(back)>1) back.pop();
	}
	// T Get(){
	// 	return op(back.top().se, front.top().se);
	// }
	mint Get(){
		mint ret = 0;
		rep(i,k) ret += back.top().se[i]*front.top().se[(k-i)%k];
		// return op(back.top().se, front.top().se);
		return ret;
	}
	int GetSize(){
		return (int)sz(back)+sz(front)-2;
	}
};


FPS op(const FPS& a,const FPS& b){
	vi idx;
	rep(i,k) if (b[i]!=0){
		idx.pb(i);
		if (sz(idx)>=3) break;
	}
	FPS ret(k);
	if (sz(idx)<=2){
		rep(i,k){
			fore(y , idx){
				ret[i] += a[(i-y+k)%k]*b[y];
			}
		}
	}else{
		assert(0);
		FPS c = a*b;
		int l = sz(c);
		rep(i,l) ret[i%k] += c[i]; 
	}
	
	return ret;
}

FPS id(){
	FPS ret(k);
	ret[0] = 1;
	return ret;
}

void solve(){
	cin>>n>>m>>k;
	swag<FPS,op,id> sw;
	vi a(n);
	rep(i,n) cin>>a[i];

	rep(i,m){
		FPS f(k);
		f[0]++;
		f[a[i]]++;
		sw.push(f);
	}
	vm ans;
	ans.pb(sw.Get()-1);
	repx(i,m,n){
		FPS f(k);
		f[0]++;
		f[a[i]]++;
		sw.push(f);
		sw.pop();
		ans.pb(sw.Get()-1);
	}
	fore(y , ans) cout << y.val() << endl;

	return;
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);

	int t = 1;
	//cin>>t;

	rep(i,t){
		solve();
	}

	return 0;
}