#931254 (D) No.1753 Don't cheat.

• 問題: No.1753 Don't cheat.
• ユーザー: 👑 hos.lyric
• 提出日時: 2023-11-24 23:21:03
• 言語: D (dmd 2.106.1)
• 結果: AC
• 実行時間: 474 ms / 3,000 ms
• コード長: 4,503 bytes
• コンパイル時間: 1,572 ms
• コンパイル使用メモリ: 152,960 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-26 09:47:26
• 合計ジャッジ時間: 11,811 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	1 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	461 ms; 5,376 KB
testcase_08	AC	470 ms; 5,376 KB
testcase_09	AC	247 ms; 5,376 KB
testcase_10	AC	474 ms; 5,376 KB
testcase_11	AC	254 ms; 5,376 KB
testcase_12	AC	440 ms; 5,376 KB
testcase_13	AC	300 ms; 5,376 KB
testcase_14	AC	402 ms; 5,376 KB
testcase_15	AC	448 ms; 5,376 KB
testcase_16	AC	335 ms; 5,376 KB
testcase_17	AC	286 ms; 5,376 KB
testcase_18	AC	241 ms; 5,376 KB
testcase_19	AC	196 ms; 5,376 KB
testcase_20	AC	348 ms; 5,376 KB
testcase_21	AC	245 ms; 5,376 KB
testcase_22	AC	293 ms; 5,376 KB
testcase_23	AC	161 ms; 5,376 KB
testcase_24	AC	261 ms; 5,376 KB
testcase_25	AC	277 ms; 5,376 KB
testcase_26	AC	305 ms; 5,376 KB
testcase_27	AC	470 ms; 5,376 KB
testcase_28	AC	472 ms; 5,376 KB
testcase_29	AC	457 ms; 5,376 KB
testcase_30	AC	456 ms; 5,376 KB
testcase_31	AC	466 ms; 5,376 KB

ソースコード

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }

string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }

struct ModInt(uint M_) {
  import std.conv : to;
  alias M = M_;
  uint x;
  this(ModInt a) { x = a.x; }
  this(uint x_) { x = x_ % M; }
  this(ulong x_) { x = cast(uint)(x_ % M); }
  this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; }
  this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); }
  ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); }
  ref ModInt opOpAssign(string op, T)(T a) {
    static if (is(T == ModInt)) {
      static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; }
      else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; }
      else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); }
      else static if (op == "/") { this *= a.inv(); }
      else static assert(false);
      return this;
    } else static if (op == "^^") {
      if (a < 0) return this = inv()^^(-a);
      ModInt b = this, c = 1U;
      for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; }
      return this = c;
    } else {
      return mixin("this " ~ op ~ "= ModInt(a)");
    }
  }
  ModInt inv() const {
    uint a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; }
    assert(a == 1); return ModInt(y);
  }
  ModInt opUnary(string op)() const {
    static if (op == "+") { return this; }
    else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; }
    else static assert(false);
  }
  ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  bool opCast(T: bool)() const { return (x != 0U); }
  string toString() const { return x.to!string; }
}

enum MO = 998244353;
alias Mint = ModInt!MO;


/*
  x: XOR
  y: EGF
  \prod[i] (cosh(P[i] y) + x^i sinh(P[i] y))
  WHT
  exp(P[i] y) or exp(-P[i] y)
*/

void main() {
  try {
    for (; ; ) {
      const N = readInt;
      auto A = new int[N + 1];
      foreach (i; 0 .. N + 1) {
        A[i] = readInt;
      }
      const sumA = A.sum;
      
      int E;
      for (; !(N < 1 << E); ++E) {}
      
      auto fs = new int[1 << E];
      void add(int i, int a) {
        foreach (j; 0 .. 1 << E) {
          fs[j] += ((popcnt(i&j)&1)?-1:+1) * a;
        }
      }
      
      foreach (i; 1 .. N + 1) {
        add(i, A[i]);
      }
      debug {
        writeln("fs = ", fs);
      }
      
      Mint ans;
      foreach (i; 0 .. N + 1) {
        // XOR = i && must choose i (if i != 0)
        Mint calc() {
          Mint ret;
          foreach (j; 0 .. 1 << E) {
            /*
              \sum[k] [y^k/k!] exp((fs[j]/sumA) y)
              = 1 / (1 - fs[j]/sumA)
            */
            ret += ((popcnt(i&j)&1)?-1:+1) * (sumA / Mint(sumA - fs[j]));
          }
          return ret;
        }
        ans += calc;
        if (i) {
          add(i, -A[i]);
          debug {
            writeln(i, ": ", fs);
          }
          ans -= calc;
          add(i, A[i]);
        }
      }
      ans /= (1 << E);
      ans *= (A[0] / Mint(sumA));
      ans = 1 - ans;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}