CF1096G Lucky Tickets [NTT, polynomial fast power]

Get stuck often get stuck often get stuck often ...

It's a naked backpack, and the violent polynomial is quickly completed. You can pass the polynomial ln / exp ...

// powered by c++11
// by Isaunoya
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize( \
    "inline,-fgcse,-fgcse-lm,-fipa-sra,-ftree-pre,-ftree-vrp,-fpeephole2,-ffast-math,-fsched-spec,unroll-loops,-falign-jumps,-falign-loops,-falign-labels,-fdevirtualize,-fcaller-saves,-fcrossjumping,-fthread-jumps,-funroll-loops,-freorder-blocks,-fschedule-insns,inline-functions,-ftree-tail-merge,-fschedule-insns2,-fstrict-aliasing,-fstrict-overflow,-falign-functions,-fcse-follow-jumps,-fsched-interblock,-fpartial-inlining,no-stack-protector,-freorder-functions,-findirect-inlining,-fhoist-adjacent-loads,-frerun-cse-after-loop,inline-small-functions,-finline-small-functions,-ftree-switch-conversion,-foptimize-sibling-calls,-fexpensive-optimizations,inline-functions-called-once,-fdelete-null-pointer-checks")

#include <bits/stdc++.h>

#define rep(i, x, y) for (register int i = (x); i <= (y); ++i)
#define Rep(i, x, y) for (register int i = (x); i >= (y); --i)

using namespace std;
using db = double;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;

using pii = pair<int, int>;

#define fir first
#define sec second

template <class T>

void cmax(T& x, const T& y) {
  if (x < y) x = y;
}

template <class T>

void cmin(T& x, const T& y) {
  if (x > y) x = y;
}

#define all(v) v.begin(), v.end()
#define sz(v) ((int)v.size())
#define pb emplace_back

template <class T>

void sort(vector<T>& v) {
  sort(all(v));
}

template <class T>

void reverse(vector<T>& v) {
  reverse(all(v));
}

template <class T>

void unique(vector<T>& v) {
  sort(all(v)), v.erase(unique(all(v)), v.end());
}

void reverse(string& s) { reverse(s.begin(), s.end()); }

const int io_size = 1 << 23 | 233;
const int io_limit = 1 << 22;
struct io_in {
  char ch;
#ifndef __WIN64
  char getchar() {
    static char buf[io_size], *p1 = buf, *p2 = buf;

    return (p1 == p2) && (p2 = (p1 = buf) + fread(buf, 1, io_size, stdin), p1 == p2) ? EOF : *p1++;
  }
#endif
  io_in& operator>>(char& c) {
    for (c = getchar(); isspace(c); c = getchar())
      ;

    return *this;
  }
  io_in& operator>>(string& s) {
    for (s.clear(); isspace(ch = getchar());)
      ;

    if (!~ch) return *this;

    for (s = ch; !isspace(ch = getchar()) && ~ch; s += ch)
      ;

    return *this;
  }

  io_in& operator>>(char* str) {
    char* cur = str;
    while (*cur) *cur++ = 0;

    for (cur = str; isspace(ch = getchar());)
      ;
    if (!~ch) return *this;

    for (*cur = ch; !isspace(ch = getchar()) && ~ch; *++cur = ch)
      ;

    return *++cur = 0, *this;
  }

  template <class T>

  void read(T& x) {
    bool f = 0;
    while ((ch = getchar()) < 48 && ~ch) f ^= (ch == 45);

    x = ~ch ? (ch ^ 48) : 0;
    while ((ch = getchar()) > 47) x = x * 10 + (ch ^ 48);
    x = f ? -x : x;
  }

  io_in& operator>>(int& x) { return read(x), *this; }

  io_in& operator>>(ll& x) { return read(x), *this; }

  io_in& operator>>(uint& x) { return read(x), *this; }

  io_in& operator>>(ull& x) { return read(x), *this; }

  io_in& operator>>(db& x) {
    read(x);
    bool f = x < 0;
    x = f ? -x : x;
    if (ch ^ '.') return *this;

    double d = 0.1;
    while ((ch = getchar()) > 47) x += d * (ch ^ 48), d *= .1;
    return x = f ? -x : x, *this;
  }
} in;

struct io_out {
  char buf[io_size], *s = buf;
  int pw[233], st[233];

  io_out() {
    set(7);
    rep(i, pw[0] = 1, 9) pw[i] = pw[i - 1] * 10;
  }

  ~io_out() { flush(); }

  void io_chk() {
    if (s - buf > io_limit) flush();
  }

  void flush() { fwrite(buf, 1, s - buf, stdout), fflush(stdout), s = buf; }

  io_out& operator<<(char c) { return *s++ = c, *this; }

  io_out& operator<<(string str) {
    for (char c : str) *s++ = c;
    return io_chk(), *this;
  }

  io_out& operator<<(char* str) {
    char* cur = str;
    while (*cur) *s++ = *cur++;
    return io_chk(), *this;
  }

  template <class T>

  void write(T x) {
    if (x < 0) *s++ = '-', x = -x;

    do {
      st[++st[0]] = x % 10, x /= 10;
    } while (x);

    while (st[0]) *s++ = st[st[0]--] ^ 48;
  }

  io_out& operator<<(int x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ll x) { return write(x), io_chk(), *this; }

  io_out& operator<<(uint x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ull x) { return write(x), io_chk(), *this; }

  int len, lft, rig;

  void set(int _length) { len = _length; }

  io_out& operator<<(db x) {
    bool f = x < 0;
    x = f ? -x : x, lft = x, rig = 1. * (x - lft) * pw[len];
    return write(f ? -lft : lft), *s++ = '.', write(rig), io_chk(), *this;
  }
} out;
#define int long long

template <int sz, int mod>

struct math_t {
  math_t() {
    fac.resize(sz + 1), ifac.resize(sz + 1);
    rep(i, fac[0] = 1, sz) fac[i] = fac[i - 1] * i % mod;

    ifac[sz] = inv(fac[sz]);
    Rep(i, sz - 1, 0) ifac[i] = ifac[i + 1] * (i + 1) % mod;
  }

  vector<int> fac, ifac;

  int qpow(int x, int y) {
    int ans = 1;
    for (; y; y >>= 1, x = x * x % mod)
      if (y & 1) ans = ans * x % mod;
    return ans;
  }

  int inv(int x) { return qpow(x, mod - 2); }

  int C(int n, int m) {
    if (n < 0 || m < 0 || n < m) return 0;
    return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
  }
};

int gcd(int x, int y) { return !y ? x : gcd(y, x % y); }
int lcm(int x, int y) { return x * y / gcd(x, y); }

const int maxn = 8e6 + 63;
const int P = 998244353;
const int G = 3;
const int Gi = 332748118;

int n, m, rev[maxn];
int a[maxn], b[maxn];
int limit = 1;
int Inv = 0;

inline int qpow(int x, int y) {
  int ans = 1;
  for (; y; y >>= 1, x = x * x % P)
    if (y & 1) ans = ans * x % P;
  return ans;
}

inline int inc(const int& x, const int& y) { return (x + y >= P) ? (x + y - P) : x + y; }
inline int dec(const int& x, const int& y) { return (x - y >= 0) ? x - y : (x - y + P); }
inline void swap(int& x, int& y) { x ^= y ^= x ^= y; }

void NTT(int* A, int type) {
  rep(i, 0, limit) if (i < rev[i]) swap(A[i], A[rev[i]]);
  for (int len = 1; len < limit; len <<= 1) {
    int Wn = qpow(type == 1 ? G : Gi, (P ^ 1) / (len << 1));
    for (int i = 0; i < limit; i += len << 1) {
      int w = 1;
      for (int j = 0, x, y; j < len; j++, w = w * Wn % P) {
        x = A[i + j], y = A[i + j + len] * w % P;
        A[i + j] = inc(x, y), A[i + j + len] = dec(x, y);
      }
    }
  }
  if (type == -1) {
    for (int i = 0; i < limit; i++) A[i] = A[i] * Inv % P;
  }
}

void init(int n) {
  limit = 1;
  int l = 0;
  while (limit <= n) {
    limit <<= 1, ++l;
  }
  for (int i = 0; i < limit; i++) rev[i] = rev[i >> 1] >> 1 | (i & 1) << l - 1;
  Inv = qpow(limit, P - 2);
}

signed main() {
  // code begin.
  in >> n >> m;
  n >>= 1;
  while (m--) {
    int x;
    in >> x;
    b[x] = 1;
  }
  a[0] = 1;
  init(10 << 2);
  while (n) {
    if (n & 1) {
      int mx = 0;
      for (int i = 0; i < limit; i++)
        if (b[i]) mx = i;
      init(mx << 2);
      NTT(a, 1), NTT(b, 1);
      for (int i = 0; i < limit; i++) a[i] = a[i] * b[i] % P;
      NTT(a, -1), NTT(b, -1);
    }
    int mx = 0;
    for (int i = 0; i < limit; i++)
      if (b[i]) mx = i;
    init(mx << 2);
    NTT(b, 1);
    for (int i = 0; i < limit; i++) b[i] = b[i] * b[i] % P;
    NTT(b, -1);
    n >>= 1;
  }
  int ans = 0;
  for (int i = 0; i < limit; i++) ans = inc(ans, (a[i] * a[i]) % P);
  out << ans << '\n';
  return 0;
  // code end.
}