結果

問題 No.1025 Modular Equation
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-04-11 00:53:14
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 1,825 ms / 5,000 ms
コード長 5,693 bytes
コンパイル時間 1,980 ms
コンパイル使用メモリ 157,208 KB
実行使用メモリ 203,336 KB
最終ジャッジ日時 2024-06-22 06:38:10
合計ジャッジ時間 24,672 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 7 ms
6,812 KB
testcase_01 AC 8 ms
6,944 KB
testcase_02 AC 8 ms
6,940 KB
testcase_03 AC 8 ms
6,944 KB
testcase_04 AC 8 ms
6,948 KB
testcase_05 AC 8 ms
6,940 KB
testcase_06 AC 8 ms
6,944 KB
testcase_07 AC 9 ms
6,944 KB
testcase_08 AC 9 ms
6,944 KB
testcase_09 AC 345 ms
6,940 KB
testcase_10 AC 359 ms
7,228 KB
testcase_11 AC 538 ms
7,140 KB
testcase_12 AC 662 ms
6,944 KB
testcase_13 AC 596 ms
6,940 KB
testcase_14 AC 663 ms
6,940 KB
testcase_15 AC 818 ms
8,592 KB
testcase_16 AC 781 ms
8,580 KB
testcase_17 AC 824 ms
7,932 KB
testcase_18 AC 770 ms
8,452 KB
testcase_19 AC 1,318 ms
96,280 KB
testcase_20 AC 1,156 ms
68,844 KB
testcase_21 AC 1,194 ms
56,384 KB
testcase_22 AC 1,101 ms
46,564 KB
testcase_23 AC 1,752 ms
193,164 KB
testcase_24 AC 443 ms
6,940 KB
testcase_25 AC 615 ms
6,944 KB
testcase_26 AC 680 ms
6,944 KB
testcase_27 AC 903 ms
7,504 KB
testcase_28 AC 878 ms
7,672 KB
testcase_29 AC 917 ms
7,176 KB
testcase_30 AC 1,368 ms
72,948 KB
testcase_31 AC 1,431 ms
104,936 KB
testcase_32 AC 1,825 ms
203,336 KB
testcase_33 AC 8 ms
6,940 KB
testcase_34 AC 11 ms
7,944 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
/home/linuxbrew/.linuxbrew/opt/dmd/include/dlang/dmd/std/numeric.d(2999): Warning: cannot inline function `std.numeric.gcdImpl!ulong.gcdImpl`

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(int M_) {
  import std.conv : to;
  alias M = M_;
  int x;
  this(ModInt a) { x = a.x; }
  this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }
  ref ModInt opAssign(long a) { return (this = ModInt(a)); }
  ref ModInt opOpAssign(string op)(ModInt a) {
    static if (op == "+") { x += a.x; if (x >= M) x -= M; }
    else static if (op == "-") { x -= a.x; if (x < 0) x += M; }
    else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }
    else static if (op == "/") { this *= a.inv(); }
    else static assert(false);
    return this;
  }
  ref ModInt opOpAssign(string op)(long a) {
    static if (op == "^^") {
      if (a < 0) return (this = inv()^^(-a));
      ModInt t2 = this, te = ModInt(1);
      for (long e = a; e > 0; e >>= 1) {
        if (e & 1) te *= t2;
        t2 *= t2;
      }
      x = cast(int)(te.x);
      return this;
    } else return mixin("this " ~ op ~ "= ModInt(a)");
  }
  ModInt inv() const {
    int a = x, b = M, y = 1, z = 0, t;
    for (; ; ) {
      t = a / b; a -= t * b;
      if (a == 0) {
        assert(b == 1 || b == -1);
        return ModInt(b * z);
      }
      y -= t * z;
      t = b / a; b -= t * a;
      if (b == 0) {
        assert(a == 1 || a == -1);
        return ModInt(a * y);
      }
      z -= t * y;
    }
  }
  ModInt opUnary(string op: "-")() const { return ModInt(-x); }
  ModInt opBinary(string op, T)(T a) const {
    return mixin("ModInt(this) " ~ op ~ "= a");
  }
  ModInt opBinaryRight(string op)(long a) const {
    return mixin("ModInt(a) " ~ op ~ "= this");
  }
  bool opCast(T: bool)() const { return (x != 0); }
  string toString() const { return x.to!string; }
}

enum MO = 10^^9 + 7;
alias Mint = ModInt!MO;

enum LIM = 2 * 10^^5 + 10;
Mint[] inv, fac, invFac;
void prepare() {
  inv = new Mint[LIM];
  fac = new Mint[LIM];
  invFac = new Mint[LIM];
  inv[1] = 1;
  foreach (i; 2 .. LIM) {
    inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)];
  }
  fac[0] = invFac[0] = 1;
  foreach (i; 1 .. LIM) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(long n, long k) {
  if (0 <= k && k <= n) {
    assert(n < LIM);
    return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
  } else {
    return Mint(0);
  }
}


/*
  m := gcd(p - 1, k)
  {g^(di) x + a g^(dj) | 0 <= j < (p-1)/d}
  = g^(di) {x + a g(d(j-i)) | 0 <= j < (p-1)/d}
  = g^(di) {x + a g(dj) | 0 <= j < (p-1)/d}
*/

void main() {
  prepare();
  
  try {
    for (; ; ) {
      const P = readLong();
      const N = readInt();
      const K = readLong();
      const B = readLong();
      auto A = new long[N];
      foreach (i; 0 .. N) {
        A[i] = readLong();
      }
      
      long g;
      auto gs = new long[P - 1];
      for (g = 2; ; ++g) {
        gs[0] = 1;
        foreach (j; 1 .. P - 1) {
          gs[j] = (gs[j - 1] * g) % P;
        }
        if (gs[1 .. P - 1].all!"a != 1") {
          break;
        }
      }
      auto ord = new long[P];
      ord[0] = -1;
      foreach (j; 0 .. P - 1) {
        ord[gs[j]] = j;
      }
      debug {
        writeln("g = ", g);
        if (P < 100) {
          writeln("ord = ", ord);
        }
      }
      
      const m = gcd(P - 1, K);
      ord[] %= m;
      
      auto dp0 = new Mint[N + 1];
      auto dp = new Mint[][](N + 1, m);
      dp0[0] = 1;
      foreach (i; 0 .. N) {
        if (A[i] == 0) {
          dp0[i + 1] = dp0[i] * P;
          dp[i + 1][] = dp[i][];
          dp[i + 1][] *= Mint(P);
        } else {
          // from zero
          {
            // add zero
            dp0[i + 1] += dp0[i];
            // add nonzero
            dp[i + 1][ord[A[i]]] += dp0[i] * (P - 1);
          }
          // from nonzero
          foreach (r; 0 .. m) {
            // add zero
            dp[i + 1][r] += dp[i][r] * ((P - 1) / m);
            // add nonzero
            for (long j = ord[A[i]]; j < P - 1; j += m) {
              long t = gs[r] + gs[j];
              if (t >= P) t -= P;
              if (t == 0) {
                dp0[i + 1] += dp[i][r] * (P - 1);
              } else {
                dp[i + 1][ord[t]] += dp[i][r] * (P - 1);
              }
            }
          }
          dp[i + 1][] *= inv[(P - 1) / m];
        }
        debug {
          writeln(dp0[i + 1], " ", dp[i + 1]);
        }
      }
      Mint ans;
      if (B == 0) {
        ans = dp0[N];
      } else {
        ans = dp[N][ord[B] % m];
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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