結果

問題 No.2144 MM
コンテスト
ユーザー hos.lyric
提出日時 2022-12-02 21:37:22
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 166 ms / 2,000 ms
コード長 5,024 bytes
コンパイル時間 1,700 ms
コンパイル使用メモリ 156,096 KB
実行使用メモリ 13,300 KB
最終ジャッジ日時 2024-06-22 16:55:08
合計ジャッジ時間 5,255 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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 * 35
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 # 

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; }
real readReal() { return readToken.to!real; }

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;



void main() {
  debug {{
    enum lim = 10;
    foreach (m; 3 .. lim + 1) {
      auto dp = new Mint[][](lim + 1, m);
      dp[0][0] = 1;
      foreach (n; 1 .. lim + 1) {
        foreach (x; 0 .. m - 1) foreach (y; 0 .. m) {
          dp[n][(x - y + m) % m] += dp[n - 1][y];
        }
      }
      writeln("m = ", m);
      foreach (n; 0 .. lim + 1) {
        writeln("  ", n, ": ", dp[n]);
      }
      foreach (n; 0 .. lim + 1) {
        foreach (x; 0 .. m) {
          Mint num = (Mint(m - 1)^^n - (-1)^^(n & 1)) / m;
          if (n % 2 == 0 && x == 0) num += 1;
          if (n % 2 != 0 && x == m - 1) num -= 1;
          assert(dp[n][x] == num);
        }
      }
    }
  }}
  
  try {
    for (; ; ) {
      const N = readInt;
      const M = readInt;
      auto A = new int[N];
      foreach (i; 0 .. N) {
        A[i] = readInt;
      }
      
      auto sums = new int[N + 1];
      foreach (i; 0 .. N) {
        sums[i + 1] = (sums[i] + (-1)^^(i & 1) * A[i]) % M;
        if (sums[i + 1] < 0) sums[i + 1] += M;
      }
      if (sums[N] != 0) {
        writeln(-1);
        continue;
      }
      
      // [0, r)
      Mint calc(int n, int r) {
        const rSave = r;
        const all = Mint(M - 1)^^n;
        const avg = (all - (-1)^^(n & 1)) / M;
        Mint ret;
        for (; r >= M; r -= M) {
          ret += all;
        }
        ret += r * avg;
        if (n & 1) {
          if (M - 1 < r) ret -= 1;
        } else {
          if (0 < r) ret += 1;
        }
        debug {
          writefln("calc %s %s = %s", n, rSave, ret);
        }
        return ret;
      }
      
      Mint ans;
      foreach (i; 0 .. N - 1) {
        int tar = (-1)^^(i & 1) * sums[i];
        if (tar < 0) tar += M;
        // [tar, tar + A[i])
        ans -= calc(N - 1 - i, tar);
        ans += calc(N - 1 - i, tar + A[i]);
      }
      ans += 1;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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