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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#706701#9526. Subsequence Countingucup-team5243RE 0ms3836kbC++1715.9kb2024-11-03 13:02:222024-11-03 13:02:22

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  • [2024-11-03 13:02:22]
  • 评测
  • 测评结果:RE
  • 用时:0ms
  • 内存:3836kb
  • [2024-11-03 13:02:22]
  • 提交

answer

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
using namespace std;

#include <cassert>
#include <utility>

namespace nachia{

template<class Elem>
struct MatrixModulo{
private:
    int h;
    int w;
    std::vector<Elem> elems;
public:
    
    MatrixModulo(int new_h=0, int new_w=0)
        : h(new_h), w(new_w), elems(h*w, Elem(0)){}
    MatrixModulo(const MatrixModulo &) = default;
    int numRow() const { return h; }
    int numColumn() const { return w; }
    int height() const { return numRow(); }
    int width() const { return numColumn(); }
    typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y*w); }
    typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y*w); }
    static MatrixModulo Identity(int n){
        auto res = MatrixModulo(n,n);
        for(int i=0; i<n; i++) res[i][i]=Elem(1);
        return res;
    }
    MatrixModulo transposed() const {
        auto res = MatrixModulo(w,h);
        for(int i=0; i<h; i++) for(int j=0; j<w; j++) res[j][i] = elems[i*w+j];
        return res;
    }
    void swapColumns(int x1, int x2){
        assert(0 <= x1 && x1 < numColumn());
        assert(0 <= x2 && x2 < numColumn());
        for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
    }
    void swapRows(int y1, int y2){
        assert(0 <= y1 && y1 < numRow());
        assert(0 <= y2 && y2 < numRow());
        for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
    }
    MatrixModulo operator*(const MatrixModulo& r) const {
        assert(width() == r.height());
        auto res = MatrixModulo(h, r.w);
        for(int i=0; i<h; i++) for(int j=0; j<w; j++) for(int k=0; k<r.w; k++){
            res[i][k] += (*this)[i][j] * r[j][k];
        }
        return res;
    }
    std::vector<Elem> operator*(const std::vector<Elem>& r) const {
        assert(width() == int(r.size()));
        auto res = std::vector<Elem>(h);
        for(int i=0; i<h; i++) for(int j=0; j<w; j++){
            res[i] += (*this)[i][j] * r[j];
        }
        return res;
    }
    Elem det() const {
        assert(height() == width());
        MatrixModulo g = *this;
        Elem ans = 1;
        for(int i=0; i<h; i++){
            int tg = -1;
            for(int j=i; j<h; j++){ if(g[j][i].val() != 0) tg = j; }
            if(tg == -1) return 0;
            if(tg != i) ans = -ans;
            for(int j=0; j<h; j++) std::swap(g[i][j], g[tg][j]);
            tg = i;
            ans *= g[i][i];
            Elem const_coeff = g[i][i].inv();
            for(int j=0; j<h; j++) g[i][j] *= const_coeff;
            for(int j=i+1; j<h; j++) for(int k=h-1; k>=i; k--) g[j][k] -= g[j][i] * g[i][k];
        }
        return ans;
    }
    int rank() const {
        if(height() == 0 || width() == 0) return 0;
        MatrixModulo g = *this;
        int y = 0;
        for(int d=0; d<w; d++){
            if(y == h) break;
            int tg = -1;
            for(int i=y; i<h; i++){ if(g[i][d].val() != 0){ tg = i; break; } }
            if(tg == -1) continue;
            for(int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]);
            tg = y;
            Elem const_coeff = g[y][d].inv();
            for(int j=d; j<w; j++) g[y][j] *= const_coeff;
            for(int i=y+1; i<h; i++) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];
            y++;
        }
        return y;
    }
    MatrixModulo pow(unsigned long long i){
        auto a = *this;
        auto res = Identity(height());
        while(i){
            if(i%2) res = res * a;
            a = a * a; i /= 2;
        }
        return res;
    }
};


} // namespace nachia

namespace nachia{

// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, a);
}

} // namespace nachia

namespace nachia{

template<unsigned int MOD>
struct StaticModint{
private:
    using u64 = unsigned long long;
    unsigned int x;
public:

    using my_type = StaticModint;
    template< class Elem >
    static Elem safe_mod(Elem x){
        if(x < 0){
            if(0 <= x+MOD) return x + MOD;
            return MOD - ((-(x+MOD)-1) % MOD + 1);
        }
        return x % MOD;
    }

    StaticModint() : x(0){}
    StaticModint(const my_type& a) : x(a.x){}
    StaticModint& operator=(const my_type&) = default;
    template< class Elem >
    StaticModint(Elem v) : x(safe_mod(v)){}
    unsigned int operator*() const noexcept { return x; }
    my_type& operator+=(const my_type& r) noexcept { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator+(const my_type& r) const noexcept { my_type res = *this; return res += r; }
    my_type& operator-=(const my_type& r) noexcept { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator-(const my_type& r) const noexcept { my_type res = *this; return res -= r; }
    my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
    my_type& operator*=(const my_type& r)noexcept { x = (u64)x * r.x % MOD; return *this; }
    my_type operator*(const my_type& r) const noexcept { my_type res = *this; return res *= r; }
    my_type pow(unsigned long long i) const noexcept {
        my_type a = *this, res = 1;
        while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
        return res;
    }
    my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
    unsigned int val() const noexcept { return x; }
    static constexpr unsigned int mod() { return MOD; }
    static my_type raw(unsigned int val) noexcept { auto res = my_type(); res.x = val; return res; }
    my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
    my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};

} // namespace nachia

namespace nachia{

template<
    class F,
    F composition(const F& f, const F& x)
>
struct DualSegtree {

    struct Node { F f; bool propagated; };
    int N;
    int logN;
    std::vector<Node> A;

    void mapf(Node& a, F f) {
        a.propagated = false;
        a.f = composition(f, a.f);
    }
    void spread(int i) {
        if(A[i].propagated || !(i < N)) return;
        mapf(A[i*2], A[i].f);
        mapf(A[i*2+1], A[i].f);
        A[i] = A[0];
    }

    DualSegtree(int n, F id) {
        N=1; logN=0;
        while(N<n){ N *= 2; logN++; }
        A.assign(N*2, { id, true });
    }
    DualSegtree(const std::vector<F>& a, F id) : DualSegtree(a.size(), id) {
        for(int i=0; i<a.size(); i++){ A[i+N].f = a[i]; A[i+N].propagated = false; }
    }

    void clear(int p) {
        p += N;
        for(int d=logN; d; d--) spread(p >> d);
        A[p] = A[0];
    }
    F get(int p){
        p += N;
        for(int d=logN; d; d--) spread(p >> d);
        return A[p].f;
    }
    void apply(int l, int r, F f){
        if(!(l < r)) return;
        if(l == 0 && r == N){ mapf(A[1], f); return; }
        l += N; r += N;
        for(int d=logN; d; d--){
            if((l >> d) << d != l) spread(l >> d);
            if((r >> d) << d != r) spread(r >> d);
        }
        while(l < r){
            if(l&1){ mapf(A[l++], f); } l /= 2;
            if(r&1){ mapf(A[--r], f); } r /= 2;
        }
    }
    void apply(int p, F f){
        p += N;
        for(int d=logN; d; d--) spread(p >> d);
        mapf(A[p], f);
    }
};

} // namespace nachia;

#include <iterator>
#include <functional>

template<class Elem> struct vec;

template<class Iter>
struct seq_view{
    using Ref = typename std::iterator_traits<Iter>::reference;
    using Elem = typename std::iterator_traits<Iter>::value_type;
    Iter a, b;
    Iter begin() const { return a; }
    Iter end() const { return b; }
    int size() const { return (int)(b-a); }
    seq_view(Iter first, Iter last) : a(first), b(last) {}
    seq_view sort() const { std::sort(a, b); return *this; }
    Ref& operator[](int x) const { return *(a+x); }
    template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {
        ret x(size()); for(int i=0; i<size(); i++) x[i] = i;
        x().sort([&](int l, int r){ return f(a[l],a[r]); });
        return x;
    }
    template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }
    template<class ret = vec<Elem>> ret cumsum() const {
        auto res = ret(size() + 1, Elem(0));
        for(int i=0; i<size(); i++) res[i+1] = res[i] + operator[](i);
        return res;
    }
    template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>
    ret rle(F eq = F()) const {
        auto x = ret();
        for(auto& a : (*this)){
            if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;
        } return x;
    }
    template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }
    Iter uni() const { return std::unique(a, b); }
    Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }
    Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }
    int lbi(const Elem& x) const { return lb(x) - a; }
    int ubi(const Elem& x) const { return ub(x) - a; }
    seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }
    template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }
    template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }
    template<class F> Iter when_true_to_false(F f) const {
        if(a == b) return a;
        return std::lower_bound(a, b, *a,
            [&](const Elem& x, const Elem&){ return f(x); });
    }
    seq_view same(Elem x) const { return { lb(x), ub(x) }; }
    template<class F> auto map(F f) const {
        vec<typename Iter::value_type> r;
        for(auto& x : *this) r.emp(f(x));
        return r;
    }
    Iter max() const { return std::max_element(a, b); }
    Iter min() const { return std::min_element(a, b); }
    template<class F = std::less<Elem>>
    Iter min(F f) const { return std::min_element(a, b, f); }
    seq_view rev() const { std::reverse(a, b); return *this; }
};

template<class Elem>
struct vec {
public:
    using Base = typename std::vector<Elem>;
    using Iter = typename Base::iterator;
    using CIter = typename Base::const_iterator;
    using View = seq_view<Iter>;
    using CView = seq_view<CIter>;

    vec(){}
    explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}
    template <class I2> vec(I2 first, I2 last) : a(first, last) {}
    vec(std::initializer_list<Elem> il) : a(std::move(il)) {}
    vec(Base b) : a(std::move(b)) {}
    operator Base() const { return a; }

    Iter begin(){ return a.begin(); }
    CIter begin() const { return a.begin(); }
    Iter end(){ return a.end(); }
    CIter end() const { return a.end(); }
    int size() const { return a.size(); }
    bool empty() const { return a.empty(); }
    Elem& back(){ return a.back(); }
    const Elem& back() const { return a.back(); }
    vec& sortuni(){ (*this)().sort(); a.erase((*this)().uni(), end()); return *this; }
    vec sortunied(){ vec x = *this; x.sortuni(); return x; }
    Iter operator()(int x){ return a.begin() + x; }
    CIter operator()(int x) const { return a.begin() + x; }
    View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }
    CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }
    View operator()(){ return (*this)(0,size()); }
    CView operator()() const { return (*this)(0,size()); }
    Elem& operator[](int x){ return a[x]; }
    const Elem& operator[](int x) const { return a[x]; }
    Base& operator*(){ return a; }
    const Base& operator*() const { return a; }
    vec& push(Elem args){
        a.push_back(std::move(args));
        return *this;
    }
    template<class... Args>
    vec& emp(Args &&... args){
        a.emplace_back(std::forward<Args>(args) ...);
        return *this;
    }
    template<class Range>
    vec& app(Range& x){ for(auto& v : x){ emp(v); } return *this; }
    Elem pop(){ Elem x = std::move(a.back()); a.pop_back(); return x; }
    void resize(int sz){ a.resize(sz); }
    void reserve(int sz){ a.reserve(sz); }
    bool operator==(const vec& r) const { return a == r.a; }
    bool operator!=(const vec& r) const { return a != r.a; }
    bool operator<(const vec& r) const { return a < r.a; }
    bool operator<=(const vec& r) const { return a <= r.a; }
    bool operator>(const vec& r) const { return a > r.a; }
    bool operator>=(const vec& r) const { return a >= r.a; }
    vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }
    template<class F> vec& filter(F f){
        int p = 0;
        for(auto& x : a) if(f(x)) std::swap(a[p++],x);
        resize(p); return *this;
    }
    vec& operator+=(const vec& r){ return app(r); }
    vec operator+(const vec& r) const { vec x = *this; x += r; return x; }
    vec operator*(int t) const { vec res; while(t--){ res += *this; } return res; }
private: Base a;
};

template<class IStr, class U, class T>
IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }
template<class IStr, class T>
IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }
template<class OStr, class T>
OStr& operator<<(OStr& os, const vec<T>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << v[i];
    } return os;
}
template<class OStr, class U, class T>
OStr& operator<<(OStr& os, const vec<std::pair<U,T>>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << '(' << v[i].first << ',' << v[i].second << ')';
    } return os;
}
using Modint = nachia::StaticModint<998244353>;
using Mat = nachia::MatrixModulo<Modint>;

Mat opmat(const Mat& f, const Mat& x){ return x * f; }

Mat solve(int X, i64 L, i64 d, vec<pair<Mat, i64>> rle){
    if(L == 1){
        return rle[0].first;
    }
    if(d*2 > L){
        vec<pair<Mat,i64>> nxrle(1, {rle[0].first,1});
        nxrle += rle().rev().col();
        nxrle.back().second -= 1;
        if(nxrle.back().second == 0) nxrle.pop();
        return solve(X, L, L-d, move(nxrle));
    }
    vec<i64> chp;
    chp.push(0);
    for(auto& [u,v] : rle) chp.push(chp.back() + v);
    vec<i64> chp_ds = chp().map([&](i64 x){ return x % d; }).sortunied();
    chp_ds.push(d);
    i64 ds_sz = chp_ds.size() - 1;
    nachia::DualSegtree<Mat, opmat> ds(ds_sz, Mat::Identity(X));
    rep(i,rle.size()){
        i64 l = chp[i];
        i64 r = chp[i+1];
        i64 lpds = chp_ds().lbi(l%d);
        i64 rpds = chp_ds().lbi(r%d);
        if(r/d == l/d){
            ds.apply(lpds, rpds, rle[i].first);
        } else {
            ds.apply(lpds, ds_sz, rle[i].first);
            ds.apply(0, ds_sz, rle[i].first.pow(r/d-l/d-1));
            ds.apply(0, rpds, rle[i].first);
        }
    }
    vec<pair<Mat, i64>> nxrle;
    rep(i,ds_sz) nxrle.push({ ds.get(i), chp_ds[i+1] - chp_ds[i] });
    return solve(X, d, d-L%d, move(nxrle));
}

void testcase(){
    i64 N, M, K, L; cin >> N >> M >> K >> L;
    vec<i64> A(M); cin >> A;
    vec<pair<Mat, i64>> rle;
    rep(i,N){
        i64 a,b; cin >> a >> b;
        Mat m = Mat::Identity(M+1);
        rep(j,M) if(A[j] == b) m[j][j+1] = 1;
        rle.push({ m, a });
    }
    i64 d = nachia::ExtGcd(K, L).first;
    auto mp = solve(M+1, L, d, rle);
    auto ans = mp[0][M];
    cout << ans.val() << '\n';
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3608kb

input:

4 2 17 27
3 1
10 3
6 1
10 3
1 1

output:

76

result:

ok single line: '76'

Test #2:

score: 0
Accepted
time: 0ms
memory: 3656kb

input:

5 3 1789 15150
555 718 726
72 555
1029 718
5807 726
1002 718
7240 555

output:

390415327

result:

ok single line: '390415327'

Test #3:

score: 0
Accepted
time: 0ms
memory: 3836kb

input:

1 1 1 1000000000
1000
1000000000 1000

output:

1755647

result:

ok single line: '1755647'

Test #4:

score: -100
Runtime Error

input:

1999 10 999999999 1000000000
944 901 986 915 979 988 947 999 969 946
198832 985
235662 982
367137 938
219700 949
166086 906
488084 905
891250 984
243743 971
253382 987
181971 935
2382 948
462701 981
4681 925
113363 916
119397 921
337742 982
427128 921
285959 986
197975 978
140753 907
167150 974
4576...

output:


result: