結果

問題 No.2846 Birthday Cake
コンテスト
ユーザー noya2
提出日時 2024-08-23 21:42:37
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 25,444 bytes
コンパイル時間 3,442 ms
コンパイル使用メモリ 270,780 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-08-23 21:42:42
合計ジャッジ時間 4,791 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 34
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
namespace noya2 {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; 
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);

constexpr long long primitive_root_constexpr(long long m){
    if (m == (1LL << 47) - (1LL << 24) + 1) return 3;
    return primitive_root_constexpr(static_cast<int>(m));
}

} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

namespace noya2{

struct barrett {
    unsigned int _m;
    unsigned long long im;
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    unsigned int umod() const { return _m; }
    unsigned int mul(unsigned int a, unsigned int b) const {
        unsigned long long z = a;
        z *= b;
        unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

template <int m>
struct static_modint {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    constexpr static_modint() : _v(0) {}
    template<std::signed_integral T>
    constexpr static_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    constexpr static_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    constexpr unsigned int val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    constexpr mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (uint)(z % umod());
        return *this;
    }
    constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = is_prime_flag<m>;
};


template <int id> struct dynamic_modint {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template<std::signed_integral T>
    dynamic_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    dynamic_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    uint val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = noya2::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

template<typename T>
concept Modint = requires (T &a){
    T::mod();
    a.inv();
    a.val();
    a.pow(declval<int>());
};

} // namespace noya2
#line 4 "c.cpp"
using mint1 = modint1000000007;
using mint2 = static_modint<1000000009>;
#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"
namespace noya2 {

template<typename mint>
struct binomial {
    binomial(int len = 300000){ extend(len); }
    static mint fact(int n){
        if (n < 0) return 0;
        while (n >= (int)_fact.size()) extend();
        return _fact[n];
    }
    static mint ifact(int n){
        if (n < 0) return 0;
        while (n >= (int)_fact.size()) extend();
        return _ifact[n];
    }
    static mint inv(int n){
        return ifact(n) * fact(n-1);
    }
    static mint C(int n, int r){
        if (!(0 <= r && r <= n)) return 0;
        return fact(n) * ifact(r) * ifact(n-r);
    }
    static mint P(int n, int r){
        if (!(0 <= r && r <= n)) return 0;
        return fact(n) * ifact(n-r);
    }
    inline mint operator()(int n, int r) { return C(n, r); }
    template<class... Cnts>
    static mint M(const Cnts&... cnts){
        return multinomial(0,1,cnts...);
    }
    static void initialize(int len = 2){
        _fact.clear();
        _ifact.clear();
        extend(len);
    }
  private:
    static mint multinomial(const int& sum, const mint& div_prod){
        if (sum < 0) return 0;
        return fact(sum) * div_prod;
    }
    template<class... Tail>
    static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){
        if (n1 < 0) return 0;
        return multinomial(sum+n1,div_prod*ifact(n1),tail...);
    }
    static inline std::vector<mint> _fact, _ifact;
    static void extend(int len = -1){
        if (_fact.empty()){
            _fact = _ifact = {1,1};
        }
        int siz = _fact.size();
        if (len == -1) len = siz * 2;
        len = (int)min<long long>(len, mint::mod() - 1);
        if (len < siz) return ;
        _fact.resize(len+1), _ifact.resize(len+1);
        for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;
        _ifact[len] = _fact[len].inv();
        for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;
    }
};

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/math/crt.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/crt.hpp"

namespace noya2 {

// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
                                    const std::vector<long long>& m) {
    assert(r.size() == m.size());
    int n = int(r.size());
    // Contracts: 0 <= r0 < m0
    long long r0 = 0, m0 = 1;
    for (int i = 0; i < n; i++) {
        assert(1 <= m[i]);
        long long r1 = safe_mod(r[i], m[i]), m1 = m[i];
        if (m0 < m1) {
            std::swap(r0, r1);
            std::swap(m0, m1);
        }
        if (m0 % m1 == 0) {
            if (r0 % m1 != r1) return {0, 0};
            continue;
        }
        // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

        // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
        // r2 % m0 = r0
        // r2 % m1 = r1
        // -> (r0 + x*m0) % m1 = r1
        // -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1)
        // -> x = (r1 - r0) / g * inv(u0) (mod u1)

        // im = inv(u0) (mod u1) (0 <= im < u1)
        long long g, im;
        std::tie(g, im) = inv_gcd(m0, m1);

        long long u1 = (m1 / g);
        // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
        if ((r1 - r0) % g) return {0, 0};

        // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
        long long x = (r1 - r0) / g % u1 * im % u1;

        // |r0| + |m0 * x|
        // < m0 + m0 * (u1 - 1)
        // = m0 + m0 * m1 / g - m0
        // = lcm(m0, m1)
        r0 += x * m0;
        m0 *= u1;  // -> lcm(m0, m1)
        if (r0 < 0) r0 += m0;
    }
    return {r0, m0};
}

// (rem, mod)
std::pair<long long, long long> crt(long long r1, long long m1){
    assert(1 <= m1);
    return {safe_mod(r1, m1), m1};
}

// (rem, mod)
template<class... Tail>
std::pair<long long, long long> crt(long long r0, long long m0, long long r1, long long m1, const Tail &... t){
    assert(1 <= m1);
    r1 = safe_mod(r1, m1);
    if (m0 < m1){
        std::swap(r0, r1);
        std::swap(m0, m1);
    }
    if (m0 % m1 == 0){
        if (r0 % m1 != r1){
            return {0, 0};
        }
        return crt(r0, m0, t...);
    }
    auto [g, im] = inv_gcd(m0, m1);
    long long u1 = (m1 / g);
    if ((r1 - r0) % g){
        return {0, 0};
    }
    long long x = (r1 - r0) / g % u1 * im % u1;
    r0 += x * m0;
    m0 *= u1;
    if (r0 < 0) r0 += m0;
    return crt(r0, m0, t...);
}


} // namespace noya2
#line 8 "c.cpp"

pii add(pii a, pii b){
    int p = a.first * b.second + a.second * b.first;
    int q = a.second * b.second;
    int g = gcd(p,q);
    return {p/g,q/g};
}

template<typename mint>
mint calc(int n, int ma){
    binomial<mint> bnm;
    vector<int> a(n);
    mint ans = 0;
    auto dfs = [&](auto sfs, int i, int pre, pii rat) -> void {
        if (i == n){
            if (rat != pii{1,1}) return ;
            mint prd = bnm.fact(n);
            for (int l = 0, r = 0; l < n; l = r){
                while (r < n && a[r] == a[l]) r++;
                prd *= bnm.ifact(r-l);
                // out(a[l],r-l);
            }
            ans += prd;
            // out(prd); out();
            return ;
        }
        for (int x = pre; x <= ma; x++){
            if (lcm(rat.second,x) > 100000) continue;
            pii nxt = add(rat,{1,x});
            if (nxt.first > nxt.second) continue;
            a[i] = x;
            sfs(sfs,i+1,x,nxt);
        }
    };
    dfs(dfs,0,1,{0,1});
    return ans;
}

ll solve1(int k, int n){
    mint1 a1 = calc<mint1>(k,n);
    mint2 a2 = calc<mint2>(k,n);
    ll ans = crt(a1.val(),mint1::mod(),a2.val(),mint2::mod()).first;
    return ans;
}

void umekomi(){
    int k, n; in(k,n);
    ll a[25][25];
a[1][1]=1;
a[1][2]=1;
a[1][3]=1;
a[1][4]=1;
a[1][5]=1;
a[1][6]=1;
a[1][7]=1;
a[1][8]=1;
a[1][9]=1;
a[1][10]=1;
a[1][11]=1;
a[1][12]=1;
a[1][13]=1;
a[1][14]=1;
a[1][15]=1;
a[1][16]=1;
a[1][17]=1;
a[1][18]=1;
a[1][19]=1;
a[1][20]=1;
a[1][21]=1;
a[1][22]=1;
a[1][23]=1;
a[1][24]=1;
a[2][2]=1;
a[2][3]=1;
a[2][4]=1;
a[2][5]=1;
a[2][6]=1;
a[2][7]=1;
a[2][8]=1;
a[2][9]=1;
a[2][10]=1;
a[2][11]=1;
a[2][12]=1;
a[2][13]=1;
a[2][14]=1;
a[2][15]=1;
a[2][16]=1;
a[2][17]=1;
a[2][18]=1;
a[2][19]=1;
a[2][20]=1;
a[2][21]=1;
a[2][22]=1;
a[2][23]=1;
a[2][24]=1;
a[3][3]=1;
a[3][4]=4;
a[3][5]=4;
a[3][6]=10;
a[3][7]=10;
a[3][8]=10;
a[3][9]=10;
a[3][10]=10;
a[3][11]=10;
a[3][12]=10;
a[3][13]=10;
a[3][14]=10;
a[3][15]=10;
a[3][16]=10;
a[3][17]=10;
a[3][18]=10;
a[3][19]=10;
a[3][20]=10;
a[3][21]=10;
a[3][22]=10;
a[3][23]=10;
a[3][24]=10;
a[4][4]=1;
a[4][5]=1;
a[4][6]=23;
a[4][7]=23;
a[4][8]=35;
a[4][9]=35;
a[4][10]=47;
a[4][11]=47;
a[4][12]=95;
a[4][13]=95;
a[4][14]=95;
a[4][15]=119;
a[4][16]=119;
a[4][17]=119;
a[4][18]=143;
a[4][19]=143;
a[4][20]=167;
a[4][21]=167;
a[4][22]=167;
a[4][23]=167;
a[4][24]=191;
a[5][5]=1;
a[5][6]=16;
a[5][7]=16;
a[5][8]=91;
a[5][9]=121;
a[5][10]=231;
a[5][11]=231;
a[5][12]=511;
a[5][13]=511;
a[5][14]=531;
a[5][15]=941;
a[5][16]=1001;
a[5][17]=1001;
a[5][18]=1321;
a[5][19]=1321;
a[5][20]=1851;
a[5][21]=2001;
a[5][22]=2001;
a[5][23]=2001;
a[5][24]=2511;
a[6][6]=1;
a[6][7]=1;
a[6][8]=106;
a[6][9]=226;
a[6][10]=667;
a[6][11]=667;
a[6][12]=2352;
a[6][13]=2352;
a[6][14]=2592;
a[6][15]=6762;
a[6][16]=7812;
a[6][17]=7812;
a[6][18]=12612;
a[6][19]=12612;
a[6][20]=20562;
a[6][21]=23622;
a[6][22]=23622;
a[6][23]=23622;
a[6][24]=33882;
a[7][7]=1;
a[7][8]=43;
a[7][9]=505;
a[7][10]=1688;
a[7][11]=1688;
a[7][12]=8828;
a[7][13]=8828;
a[7][14]=11740;
a[7][15]=37990;
a[7][16]=50205;
a[7][17]=50205;
a[7][18]=98967;
a[7][19]=98967;
a[7][20]=188049;
a[7][21]=247899;
a[7][22]=247941;
a[7][23]=247941;
a[7][24]=409165;
a[8][8]=1;
a[8][9]=309;
a[8][10]=1961;
a[8][11]=1961;
a[8][12]=20847;
a[8][13]=20847;
a[8][14]=39027;
a[8][15]=180819;
a[8][16]=298503;
a[8][17]=298503;
a[8][18]=706351;
a[8][19]=706351;
a[8][20]=1637057;
a[8][21]=2492121;
a[8][22]=2492905;
a[8][23]=2492905;
a[8][24]=4641625;
a[9][9]=1;
a[9][10]=640;
a[9][11]=640;
a[9][12]=26719;
a[9][13]=26719;
a[9][14]=87181;
a[9][15]=662821;
a[9][16]=1426678;
a[9][17]=1426678;
a[9][18]=4519408;
a[9][19]=4519408;
a[9][20]=12442024;
a[9][21]=23603800;
a[9][22]=23625220;
a[9][23]=23625220;
a[9][24]=50103058;
a[10][10]=1;
a[10][11]=1;
a[10][12]=11336;
a[10][13]=11336;
a[10][14]=118886;
a[10][15]=1676126;
a[10][16]=5314931;
a[10][17]=5314931;
a[10][18]=23098446;
a[10][19]=23098446;
a[10][20]=81943326;
a[10][21]=200197566;
a[10][22]=200631786;
a[10][23]=200631786;
a[10][24]=496822401;
a[11][11]=1;
a[11][12]=694;
a[11][13]=694;
a[11][14]=87781;
a[11][15]=2136223;
a[11][16]=12998305;
a[11][17]=12998305;
a[11][18]=90446137;
a[11][19]=90446137;
a[11][20]=429039909;
a[11][21]=1457497196;
a[11][22]=1464757108;
a[11][23]=1464757108;
a[11][24]=4403064282;
a[12][12]=1;
a[12][13]=1;
a[12][14]=26203;
a[12][15]=1562089;
a[12][16]=16990810;
a[12][17]=16990810;
a[12][18]=233499344;
a[12][19]=233499344;
a[12][20]=1740647525;
a[12][21]=8592067529;
a[12][22]=8683726163;
a[12][23]=8683726163;
a[12][24]=33370486316;
a[13][13]=1;
a[13][14]=1730;
a[13][15]=595349;
a[13][16]=11428613;
a[13][17]=11428613;
a[13][18]=359830680;
a[13][19]=359830680;
a[13][20]=5233214351;
a[13][21]=39580212205;
a[13][22]=40413510762;
a[13][23]=40413510762;
a[13][24]=209225931487;
a[14][14]=1;
a[14][15]=98281;
a[14][16]=3589041;
a[14][17]=3589041;
a[14][18]=303875573;
a[14][19]=303875573;
a[14][20]=10843887965;
a[14][21]=134817405451;
a[14][22]=140147181266;
a[14][23]=140147181266;
a[14][24]=1051662957619;
a[15][15]=1;
a[15][16]=204831;
a[15][17]=204831;
a[15][18]=120897041;
a[15][19]=120897041;
a[15][20]=14088489255;
a[15][21]=309930637885;
a[15][22]=332462625610;
a[15][23]=332462625610;
a[15][24]=4048971290390;
a[16][16]=1;
a[16][17]=1;
a[16][18]=15574653;
a[16][19]=15574653;
a[16][20]=9982510305;
a[16][21]=426337329317;
a[16][22]=484295650621;
a[16][23]=484295650621;
a[16][24]=11244715040211;
a[17][17]=1;
a[17][18]=61864;
a[17][19]=61864;
a[17][20]=2962502213;
a[17][21]=295288749243;
a[17][22]=382283766495;
a[17][23]=382283766495;
a[17][24]=20694326612398;
a[18][18]=1;
a[18][19]=1;
a[18][20]=198795808;
a[18][21]=73152855670;
a[18][22]=146218113382;
a[18][23]=146218113382;
a[18][24]=22228226842243;
a[19][19]=1;
a[19][20]=582085;
a[19][21]=6996250795;
a[19][22]=38473778130;
a[19][23]=38473778130;
a[19][24]=11390082915896;
a[20][20]=1;
a[20][21]=28282071;
a[20][22]=5684671181;
a[20][23]=5684671181;
a[20][24]=2186175253228;
a[21][21]=1;
a[21][22]=173183578;
a[21][23]=173183578;
a[21][24]=151220665303;
a[22][22]=1;
a[22][23]=1;
a[22][24]=2381965422;
a[23][23]=1;
a[23][24]=1643558;
a[24][24]=1;
    out(a[k][n]);

}

void solve(){
    umekomi(); return ;
    int mx = 24;
    // int mx = 5;
    for (int k = 1; k <= mx; k++){
        for (int n = k; n <= mx; n++){
            cout << "a[" << k << "][" << n << "]=" << solve1(k,n) << ";" << endl;
        }
    }
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
0