program_contest_library

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:heavy_check_mark: test/aoj2996.test.cpp

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Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2996"
#include "../memo/macro.hpp"
#include "../math/modint.cpp"
#include "../math/NTT.cpp"

using mint = modint<65537>;
signed main(void) {
    ll t;
    cin >> t;
    while(t--) {
        ll n;
        mint k;
        cin >> n >> k;
        vector<mint> a(n);
        REP(i, n) cin >> a[n-1-i];
        // a[i] を i! で割る
        mint inv = 1;
        FOR(i, 1, n) {
            inv *= mint(i).inv();
            a[i] *= inv;
        }
        // b[i] = (-k)^i / i!
        vector<mint> b(n);
        b[0] = 1;
        FOR(i, 1, n) b[i] = b[i-1] * (65537-k) * mint(i).inv();
        // a と b の畳み込みに i! を掛ける
        auto conv = any_mod_convolution<mint>(a, b);
        mint frac = 1;
        vector<mint> ret(n);
        REP(i, n) {
            if(i > 0) frac *= i;
            ret[i] = conv[i] * frac;
            cout << ret[i] << (i==n-1?'\n':' ');
        }
        cout << flush;
    }

    return 0;
}

#line 1 "test/aoj2996.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2996"
#line 1 "memo/macro.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using PII = pair<ll, ll>;
#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
template<typename T> void chmin(T &a, const T &b) { a = min(a, b); }
template<typename T> void chmax(T &a, const T &b) { a = max(a, b); }
struct FastIO {FastIO() { cin.tie(0); ios::sync_with_stdio(0); }}fastiofastio;
const ll INF = 1LL<<60;
#line 1 "math/modint.cpp"
// BEGIN CUT
template<ll MOD>
struct modint {
    ll x;
    modint(): x(0) {}
    modint(ll y) : x(y>=0 ? y%MOD : y%MOD+MOD) {}
    static constexpr ll mod() { return MOD; }
    // e乗
    modint pow(ll e) {
        ll a = 1, p = x;
        while(e > 0) {
            if(e%2 == 0) {p = (p*p) % MOD; e /= 2;}
            else {a = (a*p) % MOD; e--;}
        }
        return modint(a);
    }
    modint inv() const {
        ll a=x, b=MOD, u=1, y=1, v=0, z=0;
        while(a) {
            ll q = b/a;
            swap(z -= q*u, u);
            swap(y -= q*v, v);
            swap(b -= q*a, a);
        }
        return z;
    }
    // Comparators
    bool operator <(modint b) { return x < b.x; }
    bool operator >(modint b) { return x > b.x; }
    bool operator<=(modint b) { return x <= b.x; }
    bool operator>=(modint b) { return x >= b.x; }
    bool operator!=(modint b) { return x != b.x; }
    bool operator==(modint b) { return x == b.x; }
    // Basic Operations
    modint operator+(modint r) const { return modint(*this) += r; }
    modint operator-(modint r) const { return modint(*this) -= r; }
    modint operator*(modint r) const { return modint(*this) *= r; }
    modint operator/(modint r) const { return modint(*this) /= r; }
    modint &operator+=(modint r) {
        if((x += r.x) >= MOD) x -= MOD;
        return *this;
    }
    modint &operator-=(modint r) {
        if((x -= r.x) < 0) x += MOD;
        return *this;
    }
    modint &operator*=(modint r) {
    #if !defined(_WIN32) || defined(_WIN64)
        x = (ll)x * r.x % MOD; return *this;
    #endif
        unsigned long long y = (unsigned long long)x * r.x;
        unsigned xh = (unsigned) (y >> 32), xl = (unsigned) y, d, m;
        asm(
            "divl %4; \n\t"
            : "=a" (d), "=d" (m)
            : "d" (xh), "a" (xl), "r" (MOD)
        );
        x = m;
        return *this;
    }
    modint &operator/=(modint r) { return *this *= r.inv(); }
    // increment, decrement
    modint operator++() { x++; return *this; }
    modint operator++(signed) { modint t = *this; x++; return t; }
    modint operator--() { x--; return *this; }
    modint operator--(signed) { modint t = *this; x--; return t; }
    // 平方剰余のうち一つを返す なければ-1
    friend modint sqrt(modint a) {
        if(a == 0) return 0;
        ll q = MOD-1, s = 0;
        while((q&1)==0) q>>=1, s++;
        modint z=2;
        while(1) {
            if(z.pow((MOD-1)/2) == MOD-1) break;
            z++;
        }
        modint c = z.pow(q), r = a.pow((q+1)/2), t = a.pow(q);
        ll m = s;
        while(t.x>1) {
            modint tp=t;
            ll k=-1;
            FOR(i, 1, m) {
                tp *= tp;
                if(tp == 1) { k=i; break; }
            }
            if(k==-1) return -1;
            modint cp=c;
            REP(i, m-k-1) cp *= cp;
            c = cp*cp, t = c*t, r = cp*r, m = k;
        }
        return r.x;
    }

    template<class T>
    friend modint operator*(T l, modint r) { return modint(l) *= r; }
    template<class T>
    friend modint operator+(T l, modint r) { return modint(l) += r; }
    template<class T>
    friend modint operator-(T l, modint r) { return modint(l) -= r; }
    template<class T>
    friend modint operator/(T l, modint r) { return modint(l) /= r; }
    template<class T>
    friend bool operator==(T l, modint r) { return modint(l) == r; }
    template<class T>
    friend bool operator!=(T l, modint r) { return modint(l) != r; }
    // Input/Output
    friend ostream &operator<<(ostream& os, modint a) { return os << a.x; }
    friend istream &operator>>(istream& is, modint &a) { 
        is >> a.x;
        a.x = ((a.x%MOD)+MOD)%MOD;
        return is;
    }
    friend string to_frac(modint v) {
        static map<ll, PII> mp;
        if(mp.empty()) {
            mp[0] = mp[MOD] = {0, 1};
            FOR(i, 2, 1001) FOR(j, 1, i) if(__gcd(i, j) == 1) {
                mp[(modint(i) / j).x] = {i, j};
            }
        }
        auto itr = mp.lower_bound(v.x);
        if(itr != mp.begin() && v.x - prev(itr)->first < itr->first - v.x) --itr;
        string ret = to_string(itr->second.first + itr->second.second * ((int)v.x - itr->first));
        if(itr->second.second > 1) {
            ret += '/';
            ret += to_string(itr->second.second);
        }
        return ret;
    }
};
// END CUT
#line 1 "math/NTT.cpp"
// BEGIN CUT
template<class T, int primitive_root>
struct NTT {
    void ntt(vector<T>& a, int sign) {
        const int n = a.size();
        assert((n^(n&-n)) == 0);
        T g = 3; //g is primitive root of mod
        const ll mod = T::mod();
		T h = g.pow((mod-1)/n); // h^n = 1
		if(sign == -1) h = h.inv(); //h = h^-1 % mod
		//bit reverse
		int i = 0;
		for (int j = 1; j < n - 1; ++j) {
			for (int k = n >> 1; k >(i ^= k); k >>= 1);
			if (j < i) swap(a[i], a[j]);
		}
		for (int m = 1; m < n; m *= 2) {
			const int m2 = 2 * m;
			const T base = h.pow(n/m2);
			T w = 1;
            for(int x=0; x<m; ++x) {
				for (int s = x; s < n; s += m2) {
					T u = a[s];
					T d = a[s + m] * w;
					a[s] = u + d;
					a[s + m] = u - d;
				}
				w *= base;
			}
		}
    }
    void ntt(vector<T>& input) { ntt(input, 1); }
    void inv_ntt(vector<T>& input) {
        ntt(input, -1);
        const T n_inv = T((int)input.size()).inv();
        for(auto &x: input) x *= n_inv;
    }
    vector<T> convolution(const vector<T>& a, const vector<T>& b) {
        int sz = 1;
        while(sz < (int)a.size() + (int)b.size()) sz *= 2;
        vector<T> a2(a), b2(b);
        a2.resize(sz); b2.resize(sz);
        ntt(a2); ntt(b2);
        for(int i=0; i<sz; ++i) a2[i] *= b2[i];
        inv_ntt(a2);
        return a2;
    }
};

template<class T>
vector<T> any_mod_convolution(vector<T> a, vector<T> b) {
    const ll m1 = 167772161, m2 = 469762049, m3 = 1224736769;
    NTT<modint<m1>,3> ntt1;
    NTT<modint<m2>,3> ntt2;
    NTT<modint<m3>,3> ntt3;
    vector<modint<m1>> a1(a.size()), b1(b.size());
    vector<modint<m2>> a2(a.size()), b2(b.size());
    vector<modint<m3>> a3(a.size()), b3(b.size());
    for(int i=0; i<(int)a.size(); ++i) a1[i] = a[i].x, b1[i] = b[i].x;
    for(int i=0; i<(int)a.size(); ++i) a2[i] = a[i].x, b2[i] = b[i].x;
    for(int i=0; i<(int)a.size(); ++i) a3[i] = a[i].x, b3[i] = b[i].x;
    auto x = ntt1.convolution(a1, b1);
    auto y = ntt2.convolution(a2, b2);
    auto z = ntt3.convolution(a3, b3);
    const ll m1_inv_m2 = 104391568;
    const ll m12_inv_m3 = 721017874;
    const ll m12_mod = m1 * m2 % T::mod();
    vector<T> ret(x.size());
    for(int i=0; i<(int)x.size(); ++i) {
        ll v1 = (y[i].x-x[i].x) * m1_inv_m2 % m2;
        if(v1<0) v1 += m2;
        ll v2 = (z[i].x-(x[i].x+m1*v1)%m3) * m12_inv_m3 % m3;
        if(v2<0) v2 += m3;
        ret[i] = x[i].x + m1*v1 + m12_mod*v2;
    }
    return ret;
}
// END CUT
#line 5 "test/aoj2996.test.cpp"

using mint = modint<65537>;
signed main(void) {
    ll t;
    cin >> t;
    while(t--) {
        ll n;
        mint k;
        cin >> n >> k;
        vector<mint> a(n);
        REP(i, n) cin >> a[n-1-i];
        // a[i] を i! で割る
        mint inv = 1;
        FOR(i, 1, n) {
            inv *= mint(i).inv();
            a[i] *= inv;
        }
        // b[i] = (-k)^i / i!
        vector<mint> b(n);
        b[0] = 1;
        FOR(i, 1, n) b[i] = b[i-1] * (65537-k) * mint(i).inv();
        // a と b の畳み込みに i! を掛ける
        auto conv = any_mod_convolution<mint>(a, b);
        mint frac = 1;
        vector<mint> ret(n);
        REP(i, n) {
            if(i > 0) frac *= i;
            ret[i] = conv[i] * frac;
            cout << ret[i] << (i==n-1?'\n':' ');
        }
        cout << flush;
    }

    return 0;
}

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